{"id":32946,"date":"2022-04-07T11:18:53","date_gmt":"2022-04-07T05:48:53","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=32946"},"modified":"2022-04-07T11:38:52","modified_gmt":"2022-04-07T06:08:52","slug":"big-ideas-math-answers-grade-8-chapter-2","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-8-chapter-2\/","title":{"rendered":"Big Ideas Math Answers Grade 8 Chapter 2 Transformations"},"content":{"rendered":"<p>Big Ideas Math Answers Grade 8 Chapter 2 Transformations provided helps students to learn the associated lessons easily. All the Solutions provided in BIM 8th Grade Chapter 2 Transformations are aligned according to the Transformation Textbook Chapter. Students can identify the knowledge gap accordingly and improvise on them and get a good hold of the concepts. Be on the right track and achieve success in your journey of learning math. Download the <strong>Big Ideas Math Grade 8 Answers<\/strong> Chapter 2 Transformations for free of cost and clear your queries.<\/p>\n<h2>Big Ideas Math Book 8th Grade Answer Key Chapter 2 Transformations<\/h2>\n<p>Avail the handy Big Ideas Math Grade 8 Chapter 2 Transformations Solution Key over here and solve any kind of problem easily. 8th Grade Big Ideas Math Ch 2 Transformations Answers are given by experts after doing extensive research. Simply access them by clicking on the direct links available and prepare accordingly. Enhance your Problem Solving Ability and math skills with regular practice and attempt the exams with confidence.<\/p>\n<p><strong>Performance<\/strong><\/p>\n<ul>\n<li><a href=\"#Transformations_STEAM_Video\/Performance\">Transformations STEAM Video\/Performance<\/a><\/li>\n<li><a href=\"#Transformations_Getting_Ready_for_Chapter_2\">Transformations Getting Ready for Chapter 2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 1 Translations<\/strong><\/p>\n<ul>\n<li><a href=\"http:\/\/Lesson_2.1_Translations\">Lesson 2.1 Translations<\/a><\/li>\n<li><a href=\"#Translations_Homework_&amp;_Practice_2.1\">Translations Homework &amp; Practice 2.1<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 2 Reflections<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_2.2_Reflections\">Lesson 2.2 Reflections<\/a><\/li>\n<li><a href=\"#Reflections_Homework_&amp;_Practice_2.2\">Reflections Homework &amp; Practice 2.2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 3 Rotations<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_2.3_Rotations\">Lesson 2.3 Rotations<\/a><\/li>\n<li><a href=\"#Rotations_Homework_&amp;_Practice_2.3\">Rotations Homework &amp; Practice 2.3<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 4 Congruent Figures<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_2.4_Congruent_Figures\">Lesson 2.4 Congruent Figures<\/a><\/li>\n<li><a href=\"#Congruent_Figures_Homework_&amp;_Practice_2.4\">Congruent Figures Homework &amp; Practice 2.4<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 5 Dilations<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_2.5_Dilations\">Lesson 2.5 Dilations<\/a><\/li>\n<li><a href=\"#Dilations_Homework_&amp;_Practice_2.5\">Dilations Homework &amp; Practice 2.5<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 6 Similar Figures<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_2.6_Similar_Figures\">Lesson 2.6 Similar Figures<\/a><\/li>\n<li><a href=\"#Similar_Figures_Homework_&amp;_Practice_2.6\">Similar Figures Homework &amp; Practice 2.6<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 7 Perimeters and Areas of Similar Figures<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_2.7_Perimeters_and_Areas_of_Similar_Figures\">Lesson 2.7 Perimeters and Areas of Similar Figures<\/a><\/li>\n<li><a href=\"#Perimeters_and_Areas_of_Similar_Figures_Homework_&amp;_Practice_2.7\">Perimeters and Areas of Similar Figures Homework &amp; Practice 2.7<\/a><\/li>\n<\/ul>\n<p><strong>Chapter 2: Transformations\u00a0<\/strong><\/p>\n<ul>\n<li><a href=\"#Transformations_Connecting_Concepts\">Transformations Connecting Concepts<\/a><\/li>\n<li><a href=\"#Transformations_Practice_Test\">Transformations Practice Test<\/a><\/li>\n<li><a href=\"#Transformations_Cumulative_Practice\">Transformations Cumulative Practice<\/a><\/li>\n<\/ul>\n<h3><a id=\"Transformations_STEAM_Video\/Performance\"><\/a>Transformations STEAM Video\/Performance<\/h3>\n<p><strong>STEAM Video<\/strong><\/p>\n<p><strong>Shadow Puppets<\/strong><\/p>\n<p>Some puppets are controlled using strings or wires. How else can a puppet be controlled?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33268\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-1.1.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 1.1\" width=\"212\" height=\"273\" \/><\/p>\n<p><strong>Watch the STEAM Video \u201cShadow Puppets.\u201d Then answer the following questions.<\/strong><\/p>\n<p>Question 1.<br \/>\nTory and Robert are using a light source to display puppets on a screen. Tory wants to show the pig jumping from the \ufb02oor to the window. Should she use a translation, re\ufb02ection, rotation, or dilation? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33167\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-1.2.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 1.2\" width=\"380\" height=\"206\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-1.2.png 380w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-1.2-300x163.png 300w\" sizes=\"(max-width: 380px) 100vw, 380px\" \/><\/p>\n<p>Answer:<br \/>\nIn the situation given, if we translate first, we move the pre-image closer to the center of dilation than if we translate second. That will result in a different image.<\/p>\n<p>Question 2.<br \/>\nHow can Tory show the pig getting smaller as it jumps out the window?<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p><strong>Master Puppeteer<\/strong><\/p>\n<p>After completing this chapter, you will be able to use the concepts you learned to answer the questions in the STEAM Video Performance Task. You will be given the coordinates of a kite being used bya puppeteer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33168\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-1.3.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 1.3\" width=\"179\" height=\"161\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33169\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-1.4.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 1.4\" width=\"295\" height=\"368\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-1.4.png 295w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-1.4-240x300.png 240w\" sizes=\"(max-width: 295px) 100vw, 295px\" \/><br \/>\nYou will be asked to identify transformations for given movements of the kite. When might a puppeteer want to use a re\ufb02ection?<\/p>\n<h3><a id=\"Transformations_Getting_Ready_for_Chapter_2\"><\/a>Transformations Getting Ready for Chapter 2<\/h3>\n<p><strong>Getting Ready for Chapter 2<\/strong><\/p>\n<p>Chapter Exploration<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33269\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-2.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 2\" width=\"525\" height=\"103\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-2.png 525w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-2-300x59.png 300w\" sizes=\"(max-width: 525px) 100vw, 525px\" \/><\/p>\n<p>Question 1.<br \/>\nWork with a partner. Form each triangle on a geoboard.<\/p>\n<ul>\n<li>Which of the triangles are congruent to the triangle at the right?<\/li>\n<li>Measure the sides of each triangle with a ruler. Record your results in a table.<\/li>\n<li>Write a conclusion about the side lengths of triangles that are congruent.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-33270\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-3.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 3\" width=\"153\" height=\"144\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33271\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-4.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 4\" width=\"560\" height=\"320\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-4.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-4-300x171.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Answer: option d<\/p>\n<p>When two triangles are congruent they will have exactly the same three sides and exactly the same three angles. The equal sides and angles may not be in the same position<\/p>\n<p><strong>Vocabulary<\/strong><\/p>\n<p><strong>The following vocabulary terms are de\ufb01ned in this chapter. Think about what the terms might mean and record your thoughts.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33272\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-5.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 5\" width=\"523\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-5.png 523w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-5-300x33.png 300w\" sizes=\"(max-width: 523px) 100vw, 523px\" \/><\/p>\n<h3><a id=\"Lesson_2.1_Translations\"><\/a>Lesson 2.1 Translations<\/h3>\n<p><strong>EXPLORATION 1<\/strong><br \/>\n<strong>Work with a partner.<\/strong><br \/>\na. For each \ufb01gure below, draw the \ufb01gurein a coordinate plane. Then copy the \ufb01gureonto a piece of transparent paper and slide the copy to a new location in the coordinate plane. Describe the location of the copy compared to the location of the original.<\/p>\n<ul>\n<li>point<\/li>\n<li>triangle<\/li>\n<li>line segment<\/li>\n<li>rectangle<\/li>\n<li>line<\/li>\n<\/ul>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-33274\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-6.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 6\" width=\"241\" height=\"220\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33273\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-6.1.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 6.1\" width=\"155\" height=\"185\" \/><br \/>\nb. When you slide \ufb01gures, what do you notice about sides, angles, and parallel lines?<br \/>\nc. Describe the location of each point below compared to the point A(x, y).<br \/>\nB(x + 1, y + 2)<br \/>\nC(x &#8211; 3, y + 4)<br \/>\nD(x &#8211; 2, y + 3)<br \/>\nE(x + 4, y &#8211; 1)<br \/>\nd. You copy a point with coordinates (x, y) and slide it horizontally a units and vertically b units. What are the coordinates of the copy?<\/p>\n<p><strong>2.1 Lesson<\/strong><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Tell whether the blue \ufb01gure is a translation of the red \ufb01gure.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33275\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-7.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 7\" width=\"153\" height=\"91\" \/><\/p>\n<p>Answer:<br \/>\nHere in the given figure, we can see that the shape of both red and blue figures is the same but the size is different. The red figure slide to form a blue figure but it is not the same size. So blue figure is not the translation of red figure.<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33276\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-8.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 8\" width=\"161\" height=\"105\" \/><\/p>\n<p>Answer:<br \/>\nHere in the given figure, we can see that the shape of both red and blue figures is the same and also the size is the same. The red figure slide to form exactly blue figure. So blue figure is the translation of red figure.<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 3.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nThe red triangle is translated 4 units left and 2 units up. What are the coordinates of the image?<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-46946\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-Answer-Key-img_6-300x240.png\" alt=\"Big Ideas Math Grade 8 Chapter 2 Answer Key img_6\" width=\"300\" height=\"240\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-Answer-Key-img_6-300x240.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-Answer-Key-img_6.png 653w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nWe know that to translate a figure &#8216;a&#8217; units horizontally and &#8216;b&#8217; units vertically in coordinate plane, &#8216;a&#8217; is added to x-coordinate and &#8216;b&#8217; is added to y-coordinate of the vertices.<br \/>\nA(x,y) = A'(x+a, y+b)<br \/>\nThe value a and b will be positive if shift is Right and Vertical Up and the value of a and b will be negative if shift is left and vertical Down.<br \/>\nGiven: A(-2,1) B(2,5), C(1,2) and a = -4, b = 2<br \/>\nA'(-2+a, -2+b) = A'(-2-4, 1+2) = A'(-6,3)<br \/>\nB'(2+a, 5+b) = B'(2-4, 5+2) = B'(-2,7)<br \/>\nA'(1+a, 2+b) = C'(1-4, 2+2) = C'(-3,4)<br \/>\nHence the coordinate of image are A'(-6,3), B'(-2,7), C'(-3,4).<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><strong>IDENTIFYING A TRANSLATION<\/strong><br \/>\n<strong>Tell whether the blue \ufb01gure is a translation of the red \ufb01gure.<\/strong><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33277\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-9.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 9\" width=\"194\" height=\"97\" \/><\/p>\n<p>Answer:<br \/>\nHere in the given figure, we can see that the shape of both red and blue figures is the same but the size is different. The red figure slide to form a blue figure but it is not the same size. So blue figure is not the translation of red figure.<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33278\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-10.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 10\" width=\"209\" height=\"115\" \/><\/p>\n<p>Answer:<br \/>\nHere in the given figure, we can see that the shape of both red and blue figures is the same, and also the size is the same. The red figure slide to form the exactly blue figure. So blue figure is the translation of red figure.<\/p>\n<p>Question 6.<br \/>\nThe vertices of a triangle are A(2, 2), B (0, 2), and C (3, 0). Translate the triangle 1 unit left and 2 units up. What are the coordinates of the image?<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-46954\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-Grade-8-Chapter-2-img_7-300x239.png\" alt=\"Bigideas Math Answers Grade 8 Chapter 2 img_7\" width=\"300\" height=\"239\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-Grade-8-Chapter-2-img_7-300x239.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-Grade-8-Chapter-2-img_7.png 519w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nWe know that to translate a figure &#8216;a&#8217; units horizontally and &#8216;b&#8217; units vertically in coordinate plane, &#8216;a&#8217; is added to x-coordinate and &#8216;b&#8217; is added to y-coordinate of the vertices.<br \/>\nA(x,y) = A'(x+a, y+b)<br \/>\nThe value a and b will be positive if shift is Right and Vertical Up and the value of a and b will be negative if shift is left and vertical Down.<br \/>\nGiven: A(2,2) B(0,2), C(3,0) and a = -1, b = 2<br \/>\nA'(2+a, 2+b) = A'(2-1, 2+2) = A'(1,4)<br \/>\nB'(0+a, 2+b) = B'(0-1, 2+2) = B'(-1,4)<br \/>\nA'(3+a, 0+b) = C'(3-1, 0+2) = C'(2,2)<br \/>\nHence the coordinate of image are A'(1,4), B'(-1,4), C'(2,2).<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 7.<br \/>\nA neighborhood planner uses a coordinate plane to design a new neighborhood. The coordinates A(1, -1), B(1, -2), and C (2, -1) represent House A, House B, and House C. The planner decides to place a playground centered at the origin, and moves the houses to make space. House A is now located at A'(3, -4). What are the new coordinates of House B and House C when each house is moved using the same translation? Justify your answer.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-46956\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-img_8-300x214.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 img_8\" width=\"300\" height=\"214\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-img_8-300x214.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-img_8.png 561w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nWe know that to translate a figure &#8216;a&#8217; units horizontally and &#8216;b&#8217; units vertically in the coordinate plane, &#8216;a&#8217; is added to x-coordinate and &#8216;b&#8217; is added to y-coordinate of the vertices.<br \/>\nA(x,y) = A'(x+a, y+b)<br \/>\nThe value a and b will be positive if shift is Right and Vertical Up and the value of a and b will be negative if shift is left and vertical Down.<br \/>\nGiven: A(1,-1) B(1,-2), C(2,1) and A'(3,-4)<br \/>\nA'(1+a, -1+b) = A'(3,-4) So, a = 2, b = -3<br \/>\nNew coordinates of the houses are<br \/>\nB'(1+a, -2+b) = B'(1+2, -2-3) = B'(3,-5)<br \/>\nC'(2+a, -1+b) = C'(2+2, -1-3) = C'(4,-4)<br \/>\nHence the coordinate of image are B'(3,-5),C'(4,-4)<\/p>\n<p>Question 8.<br \/>\nThe locations of a quarterback and a wide receiver on a football \ufb01eld are represented in a coordinate plane. The quarterback throws the football to the point (6, -2). Use a translation to describe a path the wide receiver can take to catch the pass.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33279\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-11.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 11\" width=\"189\" height=\"188\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-11.png 189w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-11-150x150.png 150w\" sizes=\"(max-width: 189px) 100vw, 189px\" \/><\/p>\n<p>Answer:<br \/>\nCoordinate of Receiver: (1,3) and football point:(-6,-2)<br \/>\nHorizontal shift: a = x2-x1 = 6 &#8211; 1 = 5<br \/>\nVerrical shift: b = y2 &#8211; y1 = -2 &#8211; 3 = -5<br \/>\nHence the path which receiver will take 5 unit right and 5 unit down.<\/p>\n<h3><a id=\"Translations_Homework_&amp;_Practice_2.1\"><\/a>Translations Homework &amp; Practice 2.1<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Solve the equation for y.<\/strong><\/p>\n<p>Question 1.<br \/>\n6x + y = 12<\/p>\n<p>Answer:<br \/>\nGiven<br \/>\n6x + y = 12<br \/>\nSubtract 6x from both sides<br \/>\ny = 12 &#8211; 6x<br \/>\nNow arranging the terms<br \/>\ny = -6x + 12<br \/>\ny = 6 (-x + 2)<br \/>\nThus y = 6(-x + 2)<\/p>\n<p>Question 2.<br \/>\n9 = x + 3y<\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\n9 = x + 3y<br \/>\n3y = 9 &#8211; x<br \/>\nDividing by 3 on both sides<br \/>\ny = (9 &#8211; x)\/3<br \/>\ny =\u00a0 \\(\\frac{9}{3}\\) &#8211; \\(\\frac{x}{3}\\)<br \/>\nNow arranging the terms<br \/>\ny = &#8211; \\(\\frac{x}{3}\\) + 3<br \/>\nThus y = &#8211; \\(\\frac{x}{3}\\) + 3<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{1}{3}\\)x + 2y = 8<\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\n\\(\\frac{1}{3}\\)x + 2y = 8<br \/>\nSubtracting x\/3 from both sides<br \/>\n2y = 8 &#8211; \\(\\frac{x}{3}\\)<br \/>\nNow arranging the terms<br \/>\n2y = &#8211; \\(\\frac{x}{3}\\) + 8<br \/>\ny = &#8211; \\(\\frac{x}{6}\\) + 4<\/p>\n<p>Question 4.<br \/>\nYou put $550 in an account that earns 4.4% simple interest per year. How much interest do you earn in 6 months?<br \/>\nA. $1.21<br \/>\nB. $12.10<br \/>\nC. $121.00<br \/>\nD. $145.20<\/p>\n<p>Answer: $12.10<\/p>\n<p>Explanation:<br \/>\nGiven:<br \/>\nYou put $550 in an account that earns 4.4% simple interest per year.<br \/>\nPrincipal amount: P = $550<br \/>\nRate of Interest: r = 4.4%<br \/>\nTime: t = 6 months = 0.5 year<br \/>\nWe know that formula for Simple Interest is SI = prt\/100<br \/>\nSI = (550 \u00d7 4.4 \u00d7 0.5)\/100<br \/>\nSI = 1210\/100<br \/>\nSI = 12.10<br \/>\nHence the simple interest is $12.10<br \/>\nThus the correct answer is option B.<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>DESCRIBING RELATIONSHIPS<\/strong><br \/>\n<strong>For each \ufb01gure, describe the location of the blue \ufb01gurerelative to the location of the red \ufb01gure.<\/strong> (See Exploration 1, p. 43.)<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33280\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-12.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 12\" width=\"201\" height=\"190\" \/><\/p>\n<p>Answer: The path which the receiver will take is 6 units right and 3 units down.<\/p>\n<p>Explanation:<br \/>\nCoordinate of Point A: (-3,2) and Point A&#8217;: (3,-5)<br \/>\nHorizontal shift: a = x2 &#8211; x1 = 3 &#8211; (-3) = 3 + 3 = 6<br \/>\nVertical shift: b = y2 &#8211; y1 = -5 &#8211; (-2) = -5 + 2 = -3<br \/>\nHence, The path which the receiver will take is 6 units right and 3 units down.<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33281\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-13.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 13\" width=\"193\" height=\"190\" \/><\/p>\n<p>Answer: The path which receive will take is 5 units left and 2 units down.<\/p>\n<p>Explanation:<br \/>\nCoordinate of point A: (3,-2) and point A&#8217;: (-2,-4)<br \/>\nHorizontal shift: a = x2 &#8211; x1 = -2 &#8211; (3) = -2 &#8211; 3 = -5<br \/>\nVertical shift: b = y2 &#8211; y1 = -4 &#8211; (-2) = -4 + 2 = -2<br \/>\nHence, The path which receive will take is 5 unit left and 2 unit down.<\/p>\n<p><strong>IDENTIFYING A TRANSLATION<\/strong><br \/>\n<strong>Tell whether the blue \ufb01gure is a translation of the red \ufb01gure.<\/strong><\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33282\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-14.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 14\" width=\"123\" height=\"83\" \/><\/p>\n<p>Answer:<br \/>\nBlue figure is the translation of red figure.<\/p>\n<p>Explanation:<br \/>\nHere in the given figure, we can see that the shape of both blue and red figures are the same, and also the size of both the figure are the same. Also, the orientation of the blue figure is the same as the red figure. This means that the red figure sides to form the blue figure. So, the blue figure slides to form the red figure.<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33283\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-15.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 15\" width=\"202\" height=\"81\" \/><\/p>\n<p>Answer:<br \/>\nBlue figure is not the translation of the red figure.<\/p>\n<p>Explanation:<br \/>\nHere in the given figure, we can see that the shape of both blue and red figures are the same, and also the size of both the figure are the same. But the orientation of the blue figure is different from the red figure. This means that the blue figure is not the translation of the red figure.<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33284\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-16.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 16\" width=\"190\" height=\"84\" \/><\/p>\n<p>Answer:<br \/>\nBlue figure is not the translation of the red figure.<\/p>\n<p>Explanation:<br \/>\nHere in the given figure, we can see that the shape of both blue and red figures are the same, and also the size of both the figure are the same. But the orientation of the blue figure is different from the red figure. This means that the blue figure is not the translation of the red figure. The blue figure is the mirror image of the red figure.<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33285\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-17.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 17\" width=\"164\" height=\"114\" \/><\/p>\n<p>Answer:<br \/>\nBlue figure is the translation of red-figure.<\/p>\n<p>Here in the given figure, we can see that the shape of both blue and red-figure are the same, and also the size of both the figure are the same. Also, the orientation of the blue figure is the same as the red figure. This means that the red figure slides to form the blue figure. so the figure slides to form the red figure.<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33286\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-18.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 18\" width=\"160\" height=\"106\" \/><\/p>\n<p>Answer:<br \/>\nBlue figure is the translation of red-figure.<\/p>\n<p>Explanation:<br \/>\nHere in the given figure, we can see that the shape of both blue and red figures are the same, and also the size of both the figures are the same. Also, the orientation of the both figure is the same as the red figure. This means that the red figure slides to form the blue figure. So blue figure slides to form the red figure.<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33287\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-19.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 19\" width=\"168\" height=\"97\" \/><\/p>\n<p>Answer: Blue figure is not the translation of the red-figure.<\/p>\n<p>Explanation:<br \/>\nHere in the given figure we can see that the shape of both blue and red figure are same and the size of both the figure are not same. The red figure are smaller as compared to the blue figure. This means that blue figure is not the translation of red figure.<\/p>\n<p><strong>TRANSLATE A FIGURE<\/strong><br \/>\n<strong>The vertices of a triangle are L(0, 1), M(1, -2), and N(-2, 1). Draw the \ufb01gure and its image after the translation.<\/strong><\/p>\n<p>Question 13.<br \/>\n1 unit left and 6 units up<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-46223\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-img_1-300x300.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations img_1\" width=\"300\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-img_1-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-img_1-150x150.png 150w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-img_1.png 691w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>explanation:<br \/>\nWe know that to translate a figure &#8216;a&#8217; units horizontally and &#8216;b&#8217; units vertically in the coordinate plane, &#8216;a&#8217; is added to the x-coordinate and &#8216;b&#8217; is added to the y-coordinates of the vertices.<br \/>\nA(x,y) &#8211; A'(x+a, y+b)<br \/>\nThe value &#8216;a&#8217; and &#8216;b&#8217; will be positive if the shift is Right and Vertical up and the value of &#8216;a&#8217; and &#8216;b&#8217; will be negative if the shift is left and vertical down.<br \/>\nGiven:L(0,1),M(1,-2),N(-2,1)anda=-1,b=6<br \/>\nL'(0+a,1+b)=l'(0-1,1+6)=L'(-1,7)<br \/>\nM'(1+a,-2+b)=M'(1-1,1+6)=M'(0,4)<br \/>\nN'(-2+a,1+b)=N'(-3-1,1+6)=N'(-4,7)<br \/>\nHence,the coordinate of image are L'(-1,7),M'(0,4),N'(-4,7)<\/p>\n<p>Question 14.<br \/>\n5 units right<\/p>\n<p>Answer:<br \/>\nWe know that to translate a figure &#8216;a&#8217; units horizontal and &#8216;b&#8217; units vertically in the coordinate plane, &#8216;a&#8217; is added to X-coordinate and &#8216;b&#8217; is added to Y-coordinate of the vertices.<br \/>\na(x,y),=A'(x+a,y+b)<br \/>\nthe value &#8216;a&#8217; and &#8216;b&#8217; will be positive if the shift is right and vertical up and the value of &#8216;a&#8217; and &#8216;b&#8217; will be negative if shift is left and vertical down.<br \/>\nGiven:L(0,1),M(1,-2),N(-2,1)and a=5,b=0<br \/>\nL(0+a,1+b)=L'(0+5,1+0)=L'(5,1)<br \/>\nM'(1+a,-2=b)=M'(1+5,-2+0)=M'(6,-2)<br \/>\nN'(-2+a,1+b)=N'(-2+5,1+0)=N'(3,1)<br \/>\nHence the coordinate of image are L'(5,1),M'(6,-2),N'(3,1).<\/p>\n<p>Question 15.<br \/>\n(x + 2, y + 3)<\/p>\n<p>Answer:<br \/>\nWe know that to translate a figure &#8216;a&#8217; units horizontally and &#8216;b&#8217; units vertically in the coordinate plane, &#8216;a&#8217; is added to x-coordinate and &#8216;b&#8217; is added to y-coordinate of the vertices.<br \/>\nA(x,y) = A'(x+a, y+b)<br \/>\nthe value of a and b will be positive if the shift is Right and vertical Up and the value of a and b will be negative if the shift is left and vertical down.<br \/>\nGiven: L(0,1), M(1,-2), N(-2,1) and (x+2,y+3)<br \/>\nSo the value of: a = 2 and b = 3<br \/>\nL'(o + a, 1 + b) = L'(0 + 2,1 + 3) = L'(2,4)<br \/>\nM'(1+a, -2 + b) = M'(1 + 2, -2 + 3) = M'(3, 1)<br \/>\nN'(-2 + a, 1 + b) = N'(-2 + 2, 1 + 3) = N'(0, 4)<br \/>\nHence the coordinate of the image is L'(2,4), M'(3,1), N'(0,4)<\/p>\n<p>Question 16.<br \/>\n(x &#8211; 3, y &#8211; 4)<\/p>\n<p>Answer:<br \/>\nWe know that to translate a figure &#8216;a&#8217; units horizontally and &#8216;b&#8217; units vertically in the coordinate plane, &#8216;a&#8217; is added to x-coordinate and &#8216;b&#8217; is added to y-coordinate of the vertices.<br \/>\nA(x,y) = A'(x+a, y+b)<br \/>\nthe value of a and b will be positive if the shift is Right and vertical Up and the value of a and b will be negative if the shift is left and vertical down.<br \/>\nGiven: L(0,1), M(1,-2), N(-2,1) and (x-3, y-4)<br \/>\nSo the value of a = -3 and b = -4<br \/>\nL'(0 + a, 1 + b) = L'(0-3,1-4) = L'(-3,-3)<br \/>\nM'(1 + a, -2 + b) = M'(1 &#8211; 3, -2-4) = M'(-2,-6)<br \/>\nN'(-2 + a, 1 + b) = N'(-2 &#8211; 3, 1 &#8211; 4) = N'(-5, -3)<br \/>\nHence the coordinate of the image are L'(-3,-3), M'(-2,-6), N'(-5, -3)<\/p>\n<p>Question 17.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend translates point A 2 units down and 1 unit right. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33288\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-20.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 20\" width=\"317\" height=\"93\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-20.png 317w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-20-300x88.png 300w\" sizes=\"(max-width: 317px) 100vw, 317px\" \/><\/p>\n<p>Answer:<br \/>\nWe know that to translate a figure &#8216;a&#8217; units horizontally and &#8216;b&#8217; units vertically in the coordinate plane, &#8216;a&#8217; is added to x-coordinate and &#8216;b&#8217; is added to the y-coordinate of the vertices.<br \/>\nA(x,y) = A'(x+a, y+b)<br \/>\nthe value of a and b will be positive if the shift is Right and vertical Up and the value of a and b will be negative if the shift is left and vertical down.<br \/>\nGiven points,<br \/>\nA(3, 1) and a = 1, b = -2<br \/>\nA'(3+a, 1+b) = A'(3+1, 1-2) = A'(4, -1)<br \/>\nSo, the point A&#8217; translated by my friend is wrong. He has reversed the x and y coordinate for translation.<br \/>\nHence the correct translate point is A'(4,-1)<\/p>\n<p>Question 18.<br \/>\n<strong>TRANSLATING A FIGURE<\/strong><br \/>\nTranslate the triangle 4 units right and 3 units down. What are the coordinates of the image?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33289\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-21.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 21\" width=\"196\" height=\"191\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-46925\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-img_3-300x214.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations img_3\" width=\"300\" height=\"214\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-img_3-300x214.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-img_3.png 629w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nWe know that to translate a figure &#8216;a&#8217; units horizontally and &#8216;b&#8217; units vertically in the coordinate plane, &#8216;a&#8217; is added to x-coordinate and &#8216;b&#8217; is added to y-coordinate of the vertices.<br \/>\nA(x,y) = A'(x+a, y+b)<br \/>\nthe value of a and b will be positive if the shift is Right and vertical Up and the value of a and b will be negative if the shift is left and vertical down.<br \/>\nGiven points from graph: J(-1,3), K(-1,1), L(-4,1)<br \/>\nand a = 4, b = -3<br \/>\nJ'(-1 + a, 3 + b) = J'(-1+4,3-3) = J'(3,0)<br \/>\nK'(-1 + a, 1 + b) = K'(-1 + 4, 1 &#8211; 3) = K'(3,-2)<br \/>\nL'(-4 + a, 1 + b) = L'(-4 + 4, 1 &#8211; 3) = L'(0,-2)<br \/>\nHence the coordinate of image is J'(3,0), K'(3,-2), L'(0,-2)<\/p>\n<p>Question 19.<br \/>\n<strong>TRANSLATING A FIGURE<\/strong><br \/>\nTranslate the \ufb01gure 2 units left and 4 units down. What are the coordinates of the image?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33291\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-22.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 22\" width=\"199\" height=\"188\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-46929\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-img_4-262x300.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations img_4\" width=\"262\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-img_4-262x300.png 262w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-img_4.png 502w\" sizes=\"(max-width: 262px) 100vw, 262px\" \/><br \/>\nWe know that to translate a figure &#8216;a&#8217; units horizontally and &#8216;b&#8217; units vertically in the coordinate plane, &#8216;a&#8217; is added to x-coordinate and &#8216;b&#8217; is added to y-coordinate of the vertices.<br \/>\nA(x,y) = A'(x+a, y+b)<br \/>\nthe value of a and b will be positive if the shift is Right and vertical Up and the value of a and b will be negative if the shift is left and vertical down.<br \/>\nGiven: A(-1,4), B(2,3), C(3,0), D(-1,-1)<br \/>\nand a = -2, b = -4<br \/>\nA'(-1+a, 4+b) = A'(-1-2, 4-4) = A'(-3,0)<br \/>\nB'(2+a, 3+b) = B'(2-2, 3-4) = B'(0,-1)<br \/>\nC'(3+a, 0+b) = C'(3-2, 0-4) = C'(1,-4)<br \/>\nD'(-1+a, -1+b) = D'(-1-2, -1-4) = D'(-3,-5)<br \/>\nThe coordinate of image are A'(-3,0), B'(0,-1), C'(1,-4), D'(-3,-5)<\/p>\n<p><strong>DESCRIBING A TRANSLATION<\/strong><br \/>\n<strong>Describe the translation of the point to its image.<\/strong><\/p>\n<p>Question 20.<br \/>\n(3, 2) \u2192 (1,0)<\/p>\n<p>Answer:<br \/>\nWe know that to translate a figure &#8216;a&#8217; units horizontally and &#8216;b&#8217; units vertically in the coordinate plane, &#8216;a&#8217; is added to x-coordinate and &#8216;b&#8217; is added to y-coordinate of the vertices.<br \/>\nA(x,y) = A'(x+a, y+b)<br \/>\nthe value of a and b will be positive if the shift is Right and vertical Up and the value of a and b will be negative if the shift is left and vertical down.<br \/>\nCoordinate of the point A:(3,-2) and the image point A&#8217;:(1,0)<br \/>\nHorizontal shift: a = x2 &#8211; x1 = 1 &#8211; 3 = -2<br \/>\nVertical shift: b = y2 &#8211; y1 = 0 &#8211; (-2) = 0 + 2 = 2<br \/>\nHence the translation path will be 2 units left and 2 units up.<\/p>\n<p>Question 21.<br \/>\n(-8, -4) \u2192 (-3, 5)<\/p>\n<p>Answer:<br \/>\nWe know that to translate a figure &#8216;a&#8217; units horizontally and &#8216;b&#8217; units vertically in the coordinate plane, &#8216;a&#8217; is added to x-coordinate and &#8216;b&#8217; is added to y-coordinate of the vertices.<br \/>\nA(x,y) = A'(x+a, y+b)<br \/>\nthe value of a and b will be positive if the shift is Right and vertical Up and the value of a and b will be negative if the shift is left and vertical down.<br \/>\nCoordinate of the point A:(-8,-4) and the image point A&#8217;:(-3,5)<br \/>\nHorizontal shift: a = x2 &#8211; x1 = -3 &#8211; (-8) = 5<br \/>\nVertical shift: b = y2 &#8211; y1 = 5 &#8211; (-4) = 9<br \/>\nHence the translation path will be 5 units left and 9 units up.<\/p>\n<p>Question 22.<br \/>\n<strong>REASONING<\/strong><br \/>\nYou can click and drag an icon on a computer\u2019s desktop. Is this an example of a translation? Explain.<\/p>\n<p>Answer:<br \/>\nYes, the dragging of an icon on a computer&#8217;s desktop is an example of translation.<br \/>\nBecause when dragging an icon on desktop the icon directly slides and is stored in its new position. While dragging the icon there is no change in shape and size of the icon, thus fulfilling the criteria of translation.<\/p>\n<p>Question 23.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe proposed location for a new oil platform is represented in a coordinate plane by a rectangle with vertices A(1, 3), B(1, 4), C(4, 4), and D(4, -3). An inspector recommends moving the oil platform 4 units right and 2 units down. Find the coordinates of the image. Then draw the original \ufb01gureand the image in the coordinate plane.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-46938\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Answers-Chapter-2-Transformations-img_5-300x265.png\" alt=\"BIM 8th Grade Answers Chapter 2 Transformations img_5\" width=\"300\" height=\"265\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Answers-Chapter-2-Transformations-img_5-300x265.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Answers-Chapter-2-Transformations-img_5.png 660w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nWe know that to translate a figure &#8216;a&#8217; units horizontally and &#8216;b&#8217; units vertically in the coordinate plane, &#8216;a&#8217; is added to x-coordinate and &#8216;b&#8217; is added to the y-coordinate of the vertices.<br \/>\nA(x,y) = A'(x+a, y+b)<br \/>\nthe value of a and b will be positive if the shift is Right and vertical Up and the value of a and b will be negative if the shift is left and vertical down.<br \/>\nGiven: A(1,-3), B(1,4), C(4,4), D(4,-3) and a = 4, b = -2<br \/>\nA'(1+a, -3+b) = A'(1+4, -3-2) = A'(5,-5)<br \/>\nB'(1+a, 4+b) = B'(1+4, 4-2) = B'(5,2)<br \/>\nC'(4+a, 4+b) = C'(4+4, 4-2) = C'(8,2)<br \/>\nD'(4+a, -3+b) = D'(4+4, -3-2) = D'(8,-5)<br \/>\nHence the coordinate of image are A'(5,-5), B'(5,2), C'(8,2), D'(8,-5)<\/p>\n<p>Question 24.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA school of \ufb01sh translates from point F to point D.<br \/>\na. Describe the translation of the school of \ufb01sh.<br \/>\nb. Can the \ufb01shing boat make the same translation? Explain.<br \/>\nc. Describe a translation the \ufb01shing boat could make to get to point D.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33290\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-22.1.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 22.1\" width=\"202\" height=\"175\" \/><\/p>\n<p>Answer:<br \/>\na. Coordinate of the point F: (-3,2) and the point D: (2,3)<br \/>\nHorizontal shift: a = x2 &#8211; x1 = 2 &#8211; (-3) = 2 + 5 = 7<br \/>\nVertical shift: b = y2 &#8211; y1 = 3 &#8211; 2 = 1<br \/>\nHence the path of translation is 5 unit Right and 1 unit Up.<br \/>\nb. No, the fishing boat (point B) cannot make the same translation as by fish (point F). Because in path between from point B to point D the is an island which will interrupt the translation of fishing boat.<br \/>\nc. Coordinate of the point B:(-2,-1) and the point D: (2,3)<br \/>\nHorizontal shift: a = x2 &#8211; x1 = 2 &#8211; (-2) = 2 + 2 = 4<br \/>\nVerical shift: b = y2 &#8211; y1 = 3 -(-1) = 3 + 1 = 4<br \/>\nHence the path of translation is 4 unit Right and 4 unit Up.<\/p>\n<p>Question 25.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe vertices of a triangle are A(0, -3), B(2, -1), and C(3, -3). You translate the triangle 5 units right and 2 units down. Then you translate the image 3 units left and 8 units down. Is the original triangle identical to the \ufb01nal image? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nWe know that to translate a figure &#8216;a&#8217; units horizontally and &#8216;b&#8217; units vertically in the coordinate plane, &#8216;a&#8217; is added to x-coordinate and &#8216;b&#8217; is added to y-coordinate of the vertices.<br \/>\nA(x,y) = A'(x+a, y+b)<br \/>\nthe value of a and b will be positive if the shift is Right and vertical Up and the value of a and b will be negative if the shift is left and vertical down.<br \/>\nGiven: A(0,-3), B(2,-1), C(3,-3) and a1 = 5, b1 = -2<br \/>\nA'(0+a, -3+b) = A'(0+5, -3-2) = A'(5,-5)<br \/>\nB'(2+a, -1+b) = B'(2+5, -1-2) = B'(7,-3)<br \/>\nC'(3+a, -3+b) = C'(3+5,-3-2) = C'(8,-5)<br \/>\nHence the coordinate of the first image are A'(5,-5), B'(7,-3), C'(8,-5)<br \/>\nGiven: A'(5,-5), B'(7,-3), C'(8,-5) and a2 = -3, b2 = -8<br \/>\nA&#8221;(5+a, -5+b) = A&#8221;(5-3, -5-8) = A&#8221;(2,-13)<br \/>\nB&#8221;(7+a, -3+b) = B&#8221;(7-3, -3-8) = B&#8221;(4,-11)<br \/>\nC&#8221;(8+a, -5+b) = C&#8221;(8-3,-5-8) = C&#8221;(5,-13)<br \/>\nHence the coordinate of the first image are A&#8221;(2,-13), B&#8221;(4,-11), C&#8221;(5,-13)<br \/>\na = a1+a2 = 5 &#8211; 3 = 2, and b = b1 + b2 = -2 &#8211; 8 = -10<br \/>\nA'(0+a, -3+b) = A'(0+2, -3-10) = A'(2,-13)<br \/>\nB'(2+a, -1+b) = B'(2+2, -1-10) = B'(4,-11)<br \/>\nC'(3+a, -3+b) = C'(3+2,-3-10) = C'(5,-13)<br \/>\nHence the original triangle is identical to the final image. This is because we can use both the translation by finding the resultant translation.<br \/>\nFor final translation we can use:(x+2, y-10)<\/p>\n<p>Question 26.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nIn chess, a knight can move only in an L-shaped pattern:<\/p>\n<ul>\n<li>two vertical squares, then one horizontal square;<\/li>\n<li>two horizontal squares, then one vertical square;<\/li>\n<li>one vertical square, then two horizontal squares; or<\/li>\n<li>one horizontal square, then two vertical squares.<\/li>\n<\/ul>\n<p>Write a series of translations to move the knight from g8 to g5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33292\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-23.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 23\" width=\"290\" height=\"208\" \/><\/p>\n<p>Answer:<br \/>\nThe series of translation to move knight from g8 to g5<br \/>\n1. Move 1 units Right to h8 and then 2 units Down to h6<br \/>\n2. Move 2 units Left to f6 and then 1 unit Up to f7<br \/>\n3. Move 2 units Down to f5 and then 1 unit Right to g5<\/p>\n<h3><a id=\"Lesson_2.2_Reflections\"><\/a>Lesson 2.2 Reflections<\/h3>\n<p><strong>Reflecting Figures<\/strong><\/p>\n<p><strong>Work with a partner.<\/strong><br \/>\na. For each \ufb01gure below, draw the \ufb01gure in the coordinate plane. Then copy the axes and the \ufb01gure onto a piece of transparent paper. Flip the transparent paper and align the origin and the axes with the coordinate plane. For each pair of \ufb01gures, describe the line of symmetry.<\/p>\n<ul>\n<li>point<\/li>\n<li>triangle<\/li>\n<li>line segment<\/li>\n<li>rectangle<\/li>\n<li>line<\/li>\n<\/ul>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-33293\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-24.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 24\" width=\"200\" height=\"225\" \/><br \/>\nb. When you re\ufb02ect \ufb01gures, what do you notice about sides, angles, and parallel lines?<br \/>\nc. Describe the relationship between each point below and the point A(4, 7) in terms of re\ufb02ections.<br \/>\nd. A point with coordinates (x, y) is re\ufb02ected in the x-axis. What are the coordinates of the image?<br \/>\ne. Repeat part(d) when the point is re\ufb02ected in the y-axis<\/p>\n<p><strong>2.2 Lesson<\/strong><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Tell whether the blue \ufb01gure is a re\ufb02ection of the red \ufb01gure.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33294\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-25.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 25\" width=\"124\" height=\"131\" \/><\/p>\n<p>Answer: Blue figure is not the reflection of the red figure<\/p>\n<p>Explanation:<br \/>\nBy seeing the above figure we can say that the blue figure is not the mirror image of the red figure. Thus Blue figure is not the reflection of the red figure.<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33295\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-26.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 26\" width=\"132\" height=\"116\" \/><\/p>\n<p>Answer: Blue figure is the reflection of the red figure<\/p>\n<p>Explanation:<br \/>\nBy seeing the above figure we can say that the blue figure is the mirror image of the red figure. If the red figure is flipped it would form the shape of the blue figure. Thus Blue figure is the reflection of the red figure<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 3.<br \/>\nThe vertices of a rectangle are A(-4, -3), B(-4, -1), C(-1, -1), and D(-1, -3). Draw the \ufb01gure and its re\ufb02ection in (a) the x-axis and (b) the y-axis.<\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nThe vertices of a rectangle are A(-4, -3), B(-4, -1), C(-1, -1), and D(-1, -3).<br \/>\nReflection about the x-axis:<br \/>\nA(x,y) = A'(x,-y)<br \/>\nA(-4, -3) = A'(-4,3)<br \/>\nB(-4, -1) = B'(-4,1)<br \/>\nC(-1, -1) = C'(-1,1)<br \/>\nD(-1, -3) = D'(-1,3)<br \/>\nReflection through x-axis:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-47132\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-img_9i-279x300.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations img_9(i)\" width=\"279\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-img_9i-279x300.png 279w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-img_9i.png 477w\" sizes=\"(max-width: 279px) 100vw, 279px\" \/><br \/>\nReflection through y-axis:<br \/>\nA(x,y) = A'(-x,y)<br \/>\nA(-4, -3) = A'(4,-3)<br \/>\nB(-4, -1) = B'(4,-1)<br \/>\nC(-1, -1) = C'(1,-1)<br \/>\nD(-1, -3) = D'(1,-3)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-47134\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-img_9ii-300x161.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations img_9(ii)\" width=\"300\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-img_9ii-300x161.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-img_9ii.png 682w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 4.<br \/>\n<strong>REFLECTING A FIGURE<\/strong><br \/>\nThe vertices of a triangle are J(-3, -5), K(-2, 2), and L(1, -4). Draw the \ufb01gure and its re\ufb02ection in<br \/>\n(a) the x-axis and<br \/>\n(b) the y-axis.<\/p>\n<p>Answer:<br \/>\nWhen a point is reflected about the x-axis then the y coordinate becomes the opposite.<br \/>\nA(x,y) = A'(x,-y)<br \/>\nThe vertices of a triangle are J(-3, -5), K(-2, 2), and L(1, -4).<br \/>\nReflection about the x-axis:<br \/>\nJ(-3, -5) = J'(-3,5)<br \/>\nK(-2, 2) = K'(-2,-2)<br \/>\nL(1, -4) = L'(1,4)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-48642\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-img_10i-273x300.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations img_10(i)\" width=\"273\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-img_10i-273x300.png 273w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-img_10i.png 439w\" sizes=\"(max-width: 273px) 100vw, 273px\" \/><br \/>\nwhen a point is reflected about the y-axis then the x coordinate becomes the opposite.<br \/>\nA(x,y) = A'(-x,y)<br \/>\nReflection about the y-axis:<br \/>\nJ(-3, -5) = J'(3,-5)<br \/>\nK(-2, 2) = K'(2,2)<br \/>\nL(1, -4) = L'(-1,-4)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-48643\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-2-Transformations-img_10ii-297x300.png\" alt=\"BIM Grade 8 Answers Chapter 2 Transformations img_10(ii)\" width=\"297\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-2-Transformations-img_10ii-297x300.png 297w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-2-Transformations-img_10ii.png 475w\" sizes=\"(max-width: 297px) 100vw, 297px\" \/><\/p>\n<p>Question 5.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich transformation does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33296\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-27.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 27\" width=\"491\" height=\"102\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-27.png 491w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-27-300x62.png 300w\" sizes=\"(max-width: 491px) 100vw, 491px\" \/><\/p>\n<p>Answer: 3rd figure is different from other figures. Because all the other three pictures are reflections of each other except the third one. The third picture is pointed in the same direction but all the other three figures are in opposite direction.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 6.<br \/>\nYou design a logo using the \ufb01gure shown at the left. You want both the x-axis and the y-axis to be lines of re\ufb02ection. Describe how to use re\ufb02ections to complete the design. Then draw the logo in the coordinate plane.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33297\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-28.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 28\" width=\"191\" height=\"188\" \/><\/p>\n<p>Answer:<br \/>\nWhen a point is reflected about the x-axis then the y coordinate becomes the opposite.<br \/>\nA(x,y) = A'(x,-y)<br \/>\nA(-4,2), B(-2,2), C(0,0), D(-2,0)<br \/>\nReflection about the x-axis:<br \/>\nA(-4,2) = A'(-4,-2)<br \/>\nB(-2,2) = B'(-2,-2)<br \/>\nC(0,0) = C'(0,0)<br \/>\nD(-2,0) = D'(-2,0)<br \/>\nwhen a point is reflected about the y-axis then the x coordinate becomes the opposite.<br \/>\nA(x,y) = A'(-x,y)<br \/>\nReflection about the y-axis:<br \/>\nA(-4,2) = A&#8221;(4,2)<br \/>\nB(-2,2) = B&#8221;(2,2)<br \/>\nC(0,0) = C&#8221;(0,0)<br \/>\nD(-2,0) = D&#8221;(2,0)<br \/>\nNow to complete the Logo again we have to take a reflection of the image figure about the y-axis. In this way, the logo will be symmetric about both axis.<br \/>\nA&#8221;(4,2) = A&#8221;&#8216;(4,-2)<br \/>\nB&#8221;(2,2) = B&#8221;&#8216;(2,-2)<br \/>\nC&#8221;(0,0) = C&#8221;&#8216;(0,0)<br \/>\nD&#8221;(2,0) = D&#8221;&#8216;(-2,0)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-48645\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answer-Key-Grade-8-Chapter-2-img_11-300x182.png\" alt=\"Bigideas Math Answer Key Grade 8 Chapter 2 img_11\" width=\"300\" height=\"182\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answer-Key-Grade-8-Chapter-2-img_11-300x182.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answer-Key-Grade-8-Chapter-2-img_11.png 758w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 7.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou hit the golf ball along the path shown, so that its \ufb01nal location is a re\ufb02ection in the y-axis of its starting location.<br \/>\na. Does the golf ball land in the hole? Explain.<br \/>\nb. Your friend tries the shot from the same starting location. He bounces the ball of the wall at the point (-0.5, 7) so that its path is a re\ufb02ection. Does the golf ball land in the hole?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33298\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-29.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 29\" width=\"204\" height=\"202\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-29.png 204w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-29-150x150.png 150w\" sizes=\"(max-width: 204px) 100vw, 204px\" \/><\/p>\n<p>Answer:<br \/>\na. Coordinates of the location of golf ball = (2,4)<br \/>\nCoordinates of location of hole = (-3,4)<br \/>\nLocation of ball after reflection through y-axis = (2,4) = (-2,4)<br \/>\nBut the location of the hole is (-3,4)<br \/>\nSo the ball will not go into a hole and it will miss the hole by 1 unit.<br \/>\nHence the ball will not go into the hole.<br \/>\nb. Yes, when the ball bounces at the point (-0.5,7) then it will land in the hole.<\/p>\n<h3><a id=\"Reflections_Homework_&amp;_Practice_2.2\"><\/a>Reflections Homework &amp; Practice 2.2<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>The vertices of a quadrilateral are P(-1, -1), Q(0, 4), R(3, 1), and S(1, -2). Draw the figure and its image after the translation.<\/strong><\/p>\n<p>Question 1.<br \/>\n7 units down<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-48648\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Answer-Key-for-Chapter-2-img_12-261x300.png\" alt=\"Big Ideas Math 8th Grade Answer Key for Chapter 2 img_12\" width=\"261\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Answer-Key-for-Chapter-2-img_12-261x300.png 261w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Answer-Key-for-Chapter-2-img_12.png 482w\" sizes=\"(max-width: 261px) 100vw, 261px\" \/><br \/>\nWe know that to translate a figure &#8216;a&#8217; units horizontally and &#8216;b&#8217; units vertically in coordinate plane, &#8216;a&#8217; is added to x-coordinate and &#8216;b&#8217; is added to y-coordinates of the vertices.<br \/>\nA(x,y) = A'(x+a,y+b)<br \/>\nthe value &#8216;a&#8217; and &#8216;b&#8217; will be positive if shift is right and vertical up and the value of &#8216;a&#8217; and &#8216;b&#8217; will be negative if shift is left and vertical down.<br \/>\nGiven,<br \/>\nP(-1,-1)<br \/>\nQ(0,4)<br \/>\nR(3,1)<br \/>\nS(1,-2) and a = 0, b = -7<br \/>\nP'(-1+a,-1+b) = P'(-1+0,-1-7) = P'(-1,-8)<br \/>\nQ'(0+a,4+b) = Q'(0+4,4-7) = Q'(4,-3)<br \/>\nR'(3+a, 1+b) = R'(3+0,1-7) = R'(3,-6)<br \/>\nS'(1+a,-2+b) = S'(1+0,-2-7) = S'(1,-9)<br \/>\nThus the coordinate of the image is P'(-1,-8), Q'(4,-3), R'(3,-6), and S'(1,-9)<\/p>\n<p>Question 2.<br \/>\n3 units left and 2 units up<\/p>\n<p>Answer:<br \/>\nWe know that to translate a figure &#8216;a&#8217; units horizontally and &#8216;b&#8217; units vertically in coordinate plane, &#8216;a&#8217; is added to x-coordinate and &#8216;b&#8217; is added to y-coordinates of the vertices.<br \/>\nA(x,y) = A'(x+a,y+b)<br \/>\nthe value &#8216;a&#8217; and &#8216;b&#8217; will be positive if shift is right and vertical up and the value of &#8216;a&#8217; and &#8216;b&#8217; will be negative if shift is left and vertical down.<br \/>\nGiven,<br \/>\nP(-1,-1)<br \/>\nQ(0,4)<br \/>\nR(3,1)<br \/>\nS(1,-2) and a = -3, b = 2<br \/>\nP'(-1+a,-1+b) = P'(-1-3,-1+2) = P'(-4,1)<br \/>\nQ'(0+a,4+b) = Q'(0-3,4+2) = Q'(-3,6)<br \/>\nR'(3+a, 1+b) = R'(3-2,1+2) = R'(0,3)<br \/>\nS'(1+a,-2+b) = S'(1-3,-2+2) = S'(-2,0)<br \/>\nThus the coordinate of the image are P'(-4,1), Q'(-3,6), R'(0,3) and S'(-2,0)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-48661\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Ch-2-Transformations-img_11-300x293.png\" alt=\"Big Ideas Math Answers Grade 8 Ch 2 Transformations img_11\" width=\"300\" height=\"293\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Ch-2-Transformations-img_11-300x293.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Ch-2-Transformations-img_11.png 596w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 3.<br \/>\n(x + 4, y &#8211; 1)<\/p>\n<p>Answer:<br \/>\nWe know that to translate a figure &#8216;a&#8217; units horizontally and &#8216;b&#8217; units vertically in coordinate plane, &#8216;a&#8217; is added to x-coordinate and &#8216;b&#8217; is added to y-coordinates of the vertices.<br \/>\nA(x,y) = A'(x+a,y+b)<br \/>\nthe value &#8216;a&#8217; and &#8216;b&#8217; will be positive if shift is right and vertical up and the value of &#8216;a&#8217; and &#8216;b&#8217; will be negative if shift is left and vertical down.<br \/>\nGiven,<br \/>\nP(-1,-1)<br \/>\nQ(0,4)<br \/>\nR(3,1)<br \/>\nS(1,-2) and a = 4, b = -1<br \/>\nP'(-1+a,-1+b) = P'(-1+4,-1-1) = P'(3,-2)<br \/>\nQ'(0+a,4+b) = Q'(0+4,4-1) = Q'(4,3)<br \/>\nR'(3+a, 1+b) = R'(3+4,1-1) = R'(7,0)<br \/>\nS'(1+a,-2+b) = S'(1+4,-2-1) = S'(5,-3)<br \/>\nThus the coordinate of the image are P'(3,-2), Q'(4,3), R'(7,0) and S'(5,-3)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-48662\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answers-grade-8-chapter-2-transformations-img_12-300x239.png\" alt=\"Big ideas math answers grade 8 chapter 2 transformations img_12\" width=\"300\" height=\"239\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answers-grade-8-chapter-2-transformations-img_12-300x239.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answers-grade-8-chapter-2-transformations-img_12.png 641w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 4.<br \/>\n(x &#8211; 5, y &#8211; 6)<\/p>\n<p>Answer:<br \/>\nWe know that to translate a figure &#8216;a&#8217; units horizontally and &#8216;b&#8217; units vertically in coordinate plane, &#8216;a&#8217; is added to x-coordinate and &#8216;b&#8217; is added to y-coordinates of the vertices.<br \/>\nA(x,y) = A'(x+a,y+b)<br \/>\nthe value &#8216;a&#8217; and &#8216;b&#8217; will be positive if shift is right and vertical up and the value of &#8216;a&#8217; and &#8216;b&#8217; will be negative if shift is left and vertical down.<br \/>\nGiven,<br \/>\nP(-1,-1)<br \/>\nQ(0,4)<br \/>\nR(3,1)<br \/>\nS(1,-2) and a = -5, b = -6<br \/>\nP'(-1+a,-1+b) = P'(-1-5,-1-6) = P'(-6,-7)<br \/>\nQ'(0+a,4+b) = Q'(0-5,4-6) = Q'(-5,-2)<br \/>\nR'(3+a, 1+b) = R'(3-5,1-6) = R'(-2,-5)<br \/>\nS'(1+a,-2+b) = S'(1-5,-2-6) = S'(-4,-8)<br \/>\nThus the coordinate of the image are P'(-6,-7), Q'(-5,-2), R'(-2,-5) and S'(-4,-8)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-48663\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Answer-Key-Chapter-2-Transformations-img_13-292x300.png\" alt=\"BIM 8th Grade Answer Key Chapter 2 Transformations img_13\" width=\"292\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Answer-Key-Chapter-2-Transformations-img_13-292x300.png 292w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Answer-Key-Chapter-2-Transformations-img_13.png 523w\" sizes=\"(max-width: 292px) 100vw, 292px\" \/><\/p>\n<p><strong>Tell whether the angles are complementary, supplementary or neither.<\/strong><\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33299\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-30.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 30\" width=\"118\" height=\"85\" \/><\/p>\n<p>Answer:<br \/>\n108\u00b0 + 82\u00b0 = 190\u00b0<br \/>\nThus the angle is neither supplementary nor complementary.<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33300\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-31.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 31\" width=\"101\" height=\"90\" \/><\/p>\n<p>Answer: Complementary<\/p>\n<p>Explanation:<br \/>\n43\u00b0 + 47\u00b0 = 90\u00b0<br \/>\nTwo angles are called complementary when their measures add to 90 degrees.<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33301\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-32.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 32\" width=\"95\" height=\"95\" \/><\/p>\n<p>Answer:<br \/>\n38\u00b0 + 62\u00b0 = 100\u00b0<br \/>\nHence the given angle is neither supplementary nor complementary.<\/p>\n<p>Question 8.<br \/>\n36 is 75% of what number?<br \/>\nA. 27<br \/>\nB. 48<br \/>\nC. 54<br \/>\nD. 63<\/p>\n<p>Answer: B. 48<\/p>\n<p>Explanation:<br \/>\nLet x be the unknown value.<br \/>\n75% of x = 36<br \/>\n75% \u00d7 x = 36<br \/>\n75\/100 \u00d7 x = 36<br \/>\n3\/4x \u00d7 x = 36<br \/>\n3x = 36 \u00d7 4<br \/>\n3x = 144<br \/>\nx = 144\/3<br \/>\nx = 48<br \/>\nThus the correct answer is option B.<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><br \/>\n<strong>DESCRIBING RELATIONSHIPS<\/strong><br \/>\n<strong>Describe the relationship between the given point and the point A(5, 3) in terms of re\ufb02ections.<\/strong> (See Exploration 1, p. 49.)<\/p>\n<p>Answer:<br \/>\nWe know that when a point is reflected about x-axis then y-coordinate becomes the opposite.<br \/>\nP(x,y) = P'(x,-y)<br \/>\nWe know that when a point is reflected about y-axis then x-coordinate becomes opposite.<br \/>\nP(x,y) = P'(-x,y)<br \/>\nGiven: A(5,3), B(5,-3)<br \/>\nHence the point A is reflected about the x-axis to get point B.<\/p>\n<p><strong>IDENTIFYING A REFLECTION<\/strong><br \/>\n<strong>Tell whether the blue \ufb01gure is a re\ufb02ection of the red \ufb01gure.<\/strong><\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33302\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-33.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 33\" width=\"143\" height=\"105\" \/><\/p>\n<p>Answer: No<\/p>\n<p>Explanation:<br \/>\nThe blue figure is not the mirror image of the red figure. If the red figure were flipped then the right of the blue and red figure should be facing each other. So, the blue figure is not a reflection of red figure.<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33303\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-34.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 34\" width=\"130\" height=\"94\" \/><\/p>\n<p>Answer: Yes<\/p>\n<p>Explanation:<br \/>\nThe blue figure is the mirror image of the red figure. If the red figure were flipped it will result in the blue figure. So, the blue figure is a reflection of red figure.<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33304\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-35.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 35\" width=\"182\" height=\"110\" \/><\/p>\n<p>Answer: Yes<\/p>\n<p>Explanation:<br \/>\nThe blue figure is the mirror image of the red figure. If the red figure were flipped it will result in the blue figure. So, the blue figure is a reflection of red figure.<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33305\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-36.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 36\" width=\"164\" height=\"114\" \/><\/p>\n<p>Answer: No<\/p>\n<p>Explanation:<br \/>\nThe blue figure is not the mirror image of the red figure. If the red figure were flipped then the right of the blue and red figure should be facing each other. So, the blue figure is not a reflection of red figure.<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33306\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-37.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 37\" width=\"170\" height=\"113\" \/><\/p>\n<p>Answer: Yes<\/p>\n<p>Explanation:<br \/>\nThe blue figure is the mirror image of the red figure. If the red figure were flipped it will result in the blue figure. So, the blue figure is a reflection of red figure.<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33307\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-38.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 38\" width=\"122\" height=\"88\" \/><\/p>\n<p>Answer: No<\/p>\n<p>Explanation:<br \/>\nThe blue figure is not the mirror image of the red figure. If the red figure were flipped then the right of the blue and red figure should be facing each other. So, the blue figure is not a reflection of red figure.<\/p>\n<p><strong>REFLECTING FIGURES<\/strong><br \/>\n<strong>Draw the \ufb01gure and its re\ufb02ection in the x-axis. Identify the coordinates of the image.<\/strong><\/p>\n<p>Question 18.<br \/>\nA(3, 2), B(4, 4), C(1, 3)<\/p>\n<p>Answer:<br \/>\nWe know that when a point is reflected about the x-axis then y-coordinate becomes the opposite.<br \/>\nA(x,y) = A'(x,-y)<br \/>\nWe know that when a point is reflected about the y-axis then the x-coordinate becomes the opposite.<br \/>\nA(x,y) = A'(-x,y)<br \/>\nGiven,<br \/>\nA(3, 2), B(4, 4), C(1, 3)<br \/>\nReflection about the x-axis:<br \/>\nA(3, 2) = A'(3,-2)<br \/>\nB(4, 4) = B'(4,-4)<br \/>\nC(1, 3) = C'(1,-3)<br \/>\nThus the coordinate of the image are A'(3,-2), B'(4,-4), C'(1,-3)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-48671\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-Grade-8-Chapter-2-img_14-282x300.png\" alt=\"Bigideas Math Answers Grade 8 Chapter 2 img_14\" width=\"282\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-Grade-8-Chapter-2-img_14-282x300.png 282w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-Grade-8-Chapter-2-img_14.png 452w\" sizes=\"(max-width: 282px) 100vw, 282px\" \/><\/p>\n<p>Question 19.<br \/>\nM(-2, 1), N(0, 3), P(2, 2)<\/p>\n<p>Answer:<br \/>\nWe know that when a point is reflected about the x-axis then y-coordinate becomes the opposite.<br \/>\nA(x,y) = A'(x,-y)<br \/>\nWe know that when a point is reflected about the y-axis then the x-coordinate becomes the opposite.<br \/>\nA(x,y) = A'(-x,y)<br \/>\nGiven,<br \/>\nM(-2, 1), N(0, 3), P(2, 2)<br \/>\nReflection about the x-axis:<br \/>\nM(-2, 1) = M'(-2,-1)<br \/>\nN(0, 3) = N'(0,-3)<br \/>\nP(2, 2) = P'(2,-2)<br \/>\nThus the coordinate of the image are M'(-2,-1), N'(0,-3), P'(2,-2)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-48672\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Ch-2-Answer-Key-img_15-300x272.png\" alt=\"Big Ideas Math Grade 8 Ch 2 Answer Key img_15\" width=\"300\" height=\"272\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Ch-2-Answer-Key-img_15-300x272.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Ch-2-Answer-Key-img_15.png 458w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 20.<br \/>\nH(2, -2), J(4, -1), K(6, -3), L(5, -4)<\/p>\n<p>Answer:<br \/>\nWe know that when a point is reflected about the x-axis then y-coordinate becomes the opposite.<br \/>\nA(x,y) = A'(x,-y)<br \/>\nWe know that when a point is reflected about the y-axis then the x-coordinate becomes the opposite.<br \/>\nA(x,y) = A'(-x,y)<br \/>\nGiven,<br \/>\nH(2, -2), J(4, -1), K(6, -3), L(5, -4)<br \/>\nReflection about the x-axis:<br \/>\nH(2, -2) = H'(-2,-1)<br \/>\nJ(4, -1) = J'(4,1)<br \/>\nK(6, -3) = K'(6,3)<br \/>\nL(5, -4) = L'(5,4)<br \/>\nThus the coordinate of the image are H'(-2,-1), J'(4,1), K'(6,3) and L'(5,4)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-48673\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-img_16-300x291.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations img_16\" width=\"300\" height=\"291\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-img_16-300x291.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-img_16.png 485w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 21.<br \/>\nD(-2, -5), E(0, -1), F(2, -1), G(0, -5)<\/p>\n<p>Answer:<br \/>\nWe know that when a point is reflected about the x-axis then y-coordinate becomes the opposite.<br \/>\nA(x,y) = A'(x,-y)<br \/>\nWe know that when a point is reflected about the y-axis then the x-coordinate becomes the opposite.<br \/>\nA(x,y) = A'(-x,y)<br \/>\nGiven,<br \/>\nD(-2, -5), E(0, -1), F(2, -1), G(0, -5)<br \/>\nReflection about the x-axis:<br \/>\nD(-2, -5) = D'(-2,5)<br \/>\nE(0, -1) = E'(0,1)<br \/>\nF(2, -1) = F'(2,1)<br \/>\nG(0, -5) = G'(0,5)<br \/>\nThus the coordinate of the image are D'(-2,5), E'(0,1), F'(2,1), G'(0,5)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-48675\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-Math-Answers-Grade-8-Chapter-2-Transformations-img_17-252x300.png\" alt=\"Big ideas Math Answers Grade 8 Chapter 2 Transformations img_17\" width=\"252\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-Math-Answers-Grade-8-Chapter-2-Transformations-img_17-252x300.png 252w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-Math-Answers-Grade-8-Chapter-2-Transformations-img_17.png 481w\" sizes=\"(max-width: 252px) 100vw, 252px\" \/><\/p>\n<p><strong>REFLECTING FIGURES<\/strong><br \/>\n<strong>Draw the \ufb01gure and its re\ufb02ection in the y-axis. Identify the coordinates of the image.<\/strong><\/p>\n<p>Question 22.<br \/>\nQ(-4, 2), R(-2, 4), S(-1, 1)<\/p>\n<p>Answer:<br \/>\nWe know that when a point is reflected about the y-axis then the x-coordinate becomes the opposite.<br \/>\nA(x,y) = A'(-x,y)<br \/>\nGiven,<br \/>\nQ(-4, 2), R(-2, 4), S(-1, 1)<br \/>\nReflection about the x-axis:<br \/>\nQ(-4, 2) = Q'(4,2)<br \/>\nR(-2, 4) = R'(2,4)<br \/>\nS(-1, 1)= S'(1,1)<br \/>\nThus the coordinate of the image is Q'(4,2), R'(2,4), S'(1,1)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-48679\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-solution-Key-img_18-300x173.png\" alt=\"Big Ideas Math Grade 8 Chapter 2 solution Key img_18\" width=\"300\" height=\"173\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-solution-Key-img_18-300x173.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-solution-Key-img_18.png 568w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 23.<br \/>\nT(4, -2), U(4, 2), V(6, -2)<\/p>\n<p>Answer:<br \/>\nWe know that when a point is reflected about the y-axis then the x-coordinate becomes the opposite.<br \/>\nA(x,y) = A'(-x,y)<br \/>\nGiven,<br \/>\nT(4, -2), U(4, 2), V(6, -2)<br \/>\nReflection about the y-axis<br \/>\nT(4,-2) = T'(-4,-2)<br \/>\nY(4,2) = U'(-4,2)<br \/>\nV(6,-2) = V'(-6,-2)<br \/>\nThus the coordinates of the figure are T'(-4,-2), U'(-4,2), V'(-6,-2)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-48708\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-transformations-answer-key-img_19-300x156.png\" alt=\"Big Ideas Math Grade 8 Chapter 2 transformations answer key img_19\" width=\"300\" height=\"156\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-transformations-answer-key-img_19-300x156.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-transformations-answer-key-img_19.png 724w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 24.<br \/>\nW(2, -1), X(5, -2), Y(5, -5), Z(2, -4)<\/p>\n<p>Answer:<br \/>\nWe know that when a point is reflected about the y-axis then the x-coordinate becomes the opposite.<br \/>\nA(x,y) = A'(-x,y)<br \/>\nGiven,<br \/>\nW(2, -1), X(5, -2), Y(5, -5), Z(2, -4)<br \/>\nReflection about the y-axis:<br \/>\nW(2,-1) = W'(-2,-1)<br \/>\nX(5,-2) = X'(-5,-2)<br \/>\nY(5,-5) = Y'(-5,-5)<br \/>\nZ(2,-4) = Z'(-2,-4)<br \/>\nThus the coordinates of the figure are W'(-2,-1), X'(-5,-2), Y'(-5,-5), Z'(-2,-4)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-48782\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-2nd-Chapter-Answer-Key-for-Transformations-img_20-300x162.png\" alt=\"Big Ideas Math Grade 8 2nd Chapter Answer Key for Transformations img_20\" width=\"300\" height=\"162\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-2nd-Chapter-Answer-Key-for-Transformations-img_20-300x162.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-2nd-Chapter-Answer-Key-for-Transformations-img_20.png 650w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 25.<br \/>\nJ(2, 2), K(7, 4), L(9, -2), M(3, -1)<\/p>\n<p>Answer:<br \/>\nWe know that when a point is reflected about the y-axis then the x-coordinate becomes the opposite.<br \/>\nA(x,y) = A'(-x,y)<br \/>\nGiven,<br \/>\nJ(2, 2), K(7, 4), L(9, -2), M(3, -1)<br \/>\nReflection about the y-axis<br \/>\nJ(2, 2) = J(-2,2)<br \/>\nK(7, 4) = K'(-7,4)<br \/>\nL(9, -2) = L'(-9,-2)<br \/>\nM(3, -1) = M'(-3,-1)<br \/>\nThus the coordinates of the figure are J(-2,2), K'(-7,4), L'(-9,-2), M'(-3,-1)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-48823\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-2-Transformations-img_21-300x161.png\" alt=\"BIM Grade 8 Solution Key Chapter 2 Transformations img_21\" width=\"300\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-2-Transformations-img_21-300x161.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-2-Transformations-img_21.png 725w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 26.<br \/>\n<strong>REASONING<\/strong><br \/>\nWhich letters look the same when re\ufb02ected in the line?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33308\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-39.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 39\" width=\"493\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-39.png 493w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-39-300x34.png 300w\" sizes=\"(max-width: 493px) 100vw, 493px\" \/><\/p>\n<p>Answer:<br \/>\nThe letters which will look the same after being reflected through horizontal line are<br \/>\nB, C, D, E, H, I, K, O, X<\/p>\n<p><strong>STRUCTURE<\/strong><br \/>\n<strong>The coordinates of a point and its image after a re\ufb02ection are given. Identify the line of re\ufb02ection.<\/strong><\/p>\n<p>Question 27.<br \/>\n(2, -2) \u2192 (2, 2)<\/p>\n<p>Answer:<br \/>\nWhen a point is reflected about the x-axis then the y coordinate becomes the opposite.<br \/>\nA(x,y) = A'(x,-y)<br \/>\nwhen a point is reflected about the y-axis then the x coordinate becomes the opposite.<br \/>\nA(x,y) = A'(-x,y)<br \/>\nGiven A(2, -2) \u2192 A'(2, 2)<br \/>\nHere we can see that x-coordinate of both A &amp; A&#8217; is the same but the y-coordinate of A&#8217; is just the opposite of A. This means that A&#8217; is the reflection of A about the x-axis.<br \/>\nHence the point A is reflected about the x-axis to get point A&#8217;.<\/p>\n<p>Question 28.<br \/>\n(-4, 1) \u2192 (4, 1)<\/p>\n<p>Answer:<br \/>\nWhen a point is reflected about the x-axis then the y coordinate becomes the opposite.<br \/>\nA(x,y) = A'(x,-y)<br \/>\nwhen a point is reflected about the y-axis then the x coordinate becomes the opposite.<br \/>\nA(x,y) = A'(-x,y)<br \/>\nGiven A(-4, 1) \u2192 A'(4, 1)<br \/>\nHere we can see that y-coordinate of both A &amp; A&#8217; is the same but the x-coordinate of A&#8217; is just the opposite of A. This means that A&#8217; is the reflection of A about y-axis.<br \/>\nHence the point A is reflected about the y-axis to get point A&#8217;.<\/p>\n<p>Question 29.<br \/>\n(-2, -5) \u2192 (4, -5)<\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nA(-2, -5) \u2192 A'(4, -5)<br \/>\nWe observe that y-coordinate of both A and A&#8217; is same but the x-coordinate of A&#8217; is not opposite of A. This means that A&#8217; is the reflection of A about a line x = a.<br \/>\na = (x2+x1)\/2 = (4-2)\/2 = 2\/2 = 1<br \/>\nHence the point (-2,-5) is reflected about the line x = 1 to get point (4,-5)<\/p>\n<p>Question 30.<br \/>\n(-3, -4) \u2192 (-3, 0)<\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nB(-3, -4) \u2192 B'(-3, 0)<br \/>\nWe observe that x-coordinate of both B and B&#8217; is the same but the y-coordinate of B&#8217; is not the opposite of B. This means that A&#8217; is the reflection of A about a line x = a.<br \/>\nb = (y2+y1)\/2 = (0-4)\/2 = -4\/2 = -2<br \/>\nHence the point (-3,-4) is reflected about the line y = -2 to get point (-3,0)<\/p>\n<p><strong>TRANSFORMING FIGURES<\/strong><br \/>\n<strong>Find the coordinates of the \ufb01gure after the transformations.<\/strong><\/p>\n<p>Question 31.<br \/>\nTranslate the triangle 1 unit right and 5 units down. Then re\ufb02ect the image in the y-axis.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33309\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-40.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 40\" width=\"209\" height=\"195\" \/><\/p>\n<p>Answer:<br \/>\nWe know that to translate a figure &#8216;a&#8217; units horizontally and &#8216;b&#8217; units vertically in the coordinate plane, &#8216;a&#8217; is added to x-coordinate and &#8216;b&#8217; is added to y-coordinate of the vertices.<br \/>\nA(x,y) = A'(x+a, y+b)<br \/>\nThe value a and b will be positive if the shift is Right and Vertical Up and the value of a and b will be negative if the shift is left and vertical Down.<br \/>\nGiven:<br \/>\nR(-4,1)<br \/>\nS(-4,4)<br \/>\nT(-2,1)<br \/>\na = 1 and b = -5<br \/>\nR(-4,1) = R'(-4+a, 1+b) = R'(-4+1, 1-5) = R'(-3, -4)<br \/>\nS(-4,4) = S'(-4+a, 4+b) = S'(-4+1, 4-5) = S'(-3, -1)<br \/>\nT(-2,1) = T'(-2+a, 1+b) = T'(-2+1, 1-5) = T'(-1, -4)<br \/>\nThus the coordinates of the image are R'(-3, -4), S'(-3, -1), T'(-1, -4)<\/p>\n<p>Question 32.<br \/>\nRe\ufb02ect the trapezoid in the x-axis. Then translate the image 2 units left and 3 units up.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33310\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-41.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 41\" width=\"200\" height=\"198\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-41.png 200w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-41-150x150.png 150w\" sizes=\"(max-width: 200px) 100vw, 200px\" \/><\/p>\n<p>Answer:<br \/>\nWhen a point is reflected about the x-axis then the y coordinate becomes the opposite.<br \/>\nA(x,y) = A'(x,-y)<br \/>\nGiven, W(-2,-2), X(-2,1), Y(2,1), and Z(4,-2)<br \/>\n<strong>Now reflection about the x-axis:<\/strong><br \/>\nW(-2,-2) = W'(-2,2)<br \/>\nX(-2,1) = X'(-2,-1)<br \/>\nY(2,1) = Y'(2,-1)<br \/>\nZ(4,-2) = Z'(4,2)<br \/>\nThus the coordinates of the image: W'(-2,2), X'(-2,-1), Y'(2,-1), Z'(4,2)<br \/>\n<strong>Now translating the above image point:<\/strong><br \/>\nWe know that to translate a figure &#8216;a&#8217; units horizontally and &#8216;b&#8217; units vertically in the coordinate plane, &#8216;a&#8217; is added to x-coordinate and &#8216;b&#8217; is added to the y-coordinate of the vertices.<br \/>\nA(x,y) = A'(x+a, y+b)<br \/>\nThe value a and b will be positive if the shift is Right and Vertical Up and the value of a and b will be negative if the shift is left and vertical Down.<br \/>\nGiven:<br \/>\nW(-2,-2), X(-2,1), Y(2,1), and Z(4,-2)<br \/>\na = -2 and b = 3<br \/>\nW(-2,2) = W&#8221;(-2+a, 2+b) = W&#8221;(-2-2, 2+3) = W&#8221;(-4, 5)<br \/>\nX(-2,-1) = X&#8221;(-2+a, -1+b) = X&#8221;(-2-2, -1+3) = X&#8221;(-4, 2)<br \/>\nY(2,-1) = Y&#8221;(2+a, -1+b) = Y&#8221;(2-2, -1+3) = Y&#8221;(0, 2)<br \/>\nZ(4,2) = Z&#8221;(4+a, 2+b) = Z&#8221;(4-2, 2+3) = Z&#8221;(2, 5)<br \/>\nThus the coordinates of the image: W&#8221;(-4, 5), X&#8221;(-4, 2), Y&#8221;(0, 2), Z&#8221;(2, 5)<\/p>\n<p>Question 33.<br \/>\n<strong>REASONING<\/strong><br \/>\nIn Exercises 31 and 32, is the original \ufb01gure identical to the \ufb01nal image? Explain.<\/p>\n<p>Answer: Yes, in exercises 31 and 32 the original figure is identical to the final image. Because the type of transformation used is reflection and translation. The shape and size of the image figure do not change when there is reflection or translation. The only position of the image changes in both cases when compared to the position of the original figure.<\/p>\n<p>Question 34.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nHold a mirror to the left side of the photo of the vehicle.<br \/>\na. What word do you see in the mirror?<\/p>\n<p>Answer: The word which we will see in the mirror will be AMBULANCE. Because the word is written in mirror image form on the vehicle.<\/p>\n<p>b. Why do you think it is written that way on the front of the vehicle?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33311\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-42.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 42\" width=\"189\" height=\"195\" \/><\/p>\n<p>Answer: Ambulance<\/p>\n<p>Explanation:<br \/>\nIt is written in that way because the ambulance will be behind any vehicle then the word &#8220;AMBULANCE&#8221; will correctly appear in the Rear-view mirror of the front vehicle.<\/p>\n<p>Question 35.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nRe\ufb02ect the triangle in the line y = x. How are the x- and y-coordinates of the image related to the x- and y-coordinates of the original triangle?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33312\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-43.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 43\" width=\"194\" height=\"158\" \/><\/p>\n<p>Answer:<br \/>\nWhen a point is reflected about the line y = x then both x and y-coordinate become opposite.<br \/>\nA(x, y) = A'(-x, -y)<br \/>\nGiven,<br \/>\nD(-1,-3)<br \/>\nE(-1,1)<br \/>\nF(-3,1)<br \/>\nReflection about the line y = x<br \/>\nD(-1,-3) = D'(1,-3)<br \/>\nE(-1,1) = E'(1,-1)<br \/>\nF(-3,1) = F'(3,-1)<br \/>\nHence the coordinates of the image: D'(1,-3), E'(1,-1), F'(3,-1)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-48887\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-Solution-Key-img_21-300x249.png\" alt=\"Big Ideas Math Grade 8 Chapter 2 Solution Key img_21\" width=\"300\" height=\"249\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-Solution-Key-img_21-300x249.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-Solution-Key-img_21.png 658w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<h3><a id=\"Lesson_2.3_Rotations\"><\/a>Lesson 2.3 Rotations<\/h3>\n<p><strong>EXPLORATION 1<\/strong><br \/>\n<strong>Work with a partner.<\/strong><br \/>\na. For each \ufb01gurebelow, draw the \ufb01gure in the coordinate plane. Then copy the axes and the \ufb01gure onto a piece of transparent paper. Turn the transparent paper and align the origin and the axes with the coordinate plane. For each pair of \ufb01gures, describe the angle of rotation.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33313\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-44.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 44\" width=\"158\" height=\"164\" \/><\/p>\n<ul>\n<li>point<\/li>\n<li>triangle<\/li>\n<li>line segment<\/li>\n<li>rectangle<\/li>\n<\/ul>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-33314\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-45.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 45\" width=\"241\" height=\"218\" \/><br \/>\nb. When you rotate \ufb01gures, what do you notice about sides, angles, and parallel lines?<br \/>\nc. Describe the relationship between each point below and the point A(3, 6) in terms of rotations.<br \/>\nd. What are the coordinates of a point P(x, y) after a rotation 90\u00b0 counterclockwise about the origin? 180\u00b0? 270\u00b0?<\/p>\n<p><strong>2.3 Lesson<\/strong><\/p>\n<p><strong>Try It<\/strong><br \/>\n<strong>Tell whether the blue \ufb01gure is a rotation of the red \ufb01gure about the origin. If so, give the angle and direction of rotation.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33315\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-46.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 46\" width=\"202\" height=\"195\" \/><\/p>\n<p>Answer: Yes blue figure is the rotation of red figure about the origin.<\/p>\n<p>Explanation:<br \/>\nWhen we rotate the red figure 180 degrees clockwise or anti-clockwise about the origin we will get the same figure as the blue figure.<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33316\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-47.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 47\" width=\"200\" height=\"195\" \/><\/p>\n<p>Answer: Blue figure is not the rotation of the red figure.<\/p>\n<p>Explanation:<br \/>\nWhen the red figure is rotated about the origin in any direction the distance of the center point of both the red figure and the blue figure will be the same from the origin point (0,0). The distance between the center of the object and the center of rotation always remains the same.<br \/>\nThus Blue figure is not the rotation of the red figure.<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>The vertices of a \ufb01gure are given. Rotate the \ufb01gure as described. Find the coordinates of the image.<\/strong><\/p>\n<p>Question 3.<br \/>\nJ(-4, -4), K(-4, 2), L(-1, 0), M(-2, -3); 180\u00b0 about the origin<\/p>\n<p>Answer:<br \/>\nWhen a point is rotated 180 degrees about the origin then both x and y-coordinates become opposite.<br \/>\nA(x, y) = A'(-x, -y)<br \/>\nGiven, J(-4, -4), K(-4, 2), L(-1, 0), M(-2, -3)<br \/>\nRotation about the origin<br \/>\nJ(-4, -4) = J'(4,4)<br \/>\nK(-4, 2) = K'(4,-2)<br \/>\nL(-1, 0) = L'(1,0)<br \/>\nM(-2, -3) = M'(2,3)<br \/>\nHence the coordinate of the image are J'(4,4), K'(4,-2), L'(1,0), M'(2,3)<\/p>\n<p>Question 4.<br \/>\nP(-3, 2), Q(6, 1), R(-1, -5); 90\u00b0 counterclockwise about the origin<\/p>\n<p>Answer:<br \/>\nWhen a point is rotated 90 degrees about the origin then both x and y-coordinates become opposite.<br \/>\nA(x, y) = A'(-y, x)<br \/>\nGiven,<br \/>\nP(-3, 2), Q(6, 1), R(-1, -5)<br \/>\nRotation about the origin<br \/>\nP(-3, 2) = P'(-2,-3)<br \/>\nQ(6, 1) = Q'(-1,6)<br \/>\nR(-1, -5) = R'(5,-1)<br \/>\nHence the coordinate of the image is P'(-2,-3), Q'(-1,6), R'(5,-1)<\/p>\n<p>Question 5.<br \/>\nA(5, 3), B(4, -1), C(1, -1); 90\u00b0 clockwise about the origin<\/p>\n<p>Answer:<br \/>\nWhen a point is rotated 270 degrees counterclockwise about the origin then both x and y-coordinates gets interchanged and the x-coordinate becomes the opposite.<br \/>\nA(x, y) = A'(y, -x)<br \/>\nGiven,<br \/>\nA(5, 3), B(4, -1), C(1, -1)<br \/>\nRotation about the origin<br \/>\nA(5, 3) = A'(3,-5)<br \/>\nB(4, -1) = B'(-1,-4)<br \/>\nC(1, -1) = C'(-1,-1)<br \/>\nHence the coordinate of the image are A'(3,-5), B'(-1,-4), C'(-1,-1)<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 6.<br \/>\nThe vertices of a triangle are P(-1, 2), Q(-1, 0), and R(2, 0). Rotate the triangle 180\u00b0 about the origin, and then re\ufb02ect it in the x-axis. What are the coordinates of the image?<\/p>\n<p>Answer:<br \/>\nWhen a point is rotated 180 degrees about the origin then both x and y-coordinates become opposite.<br \/>\nA(x, y) = A'(-x, -y)<br \/>\nGiven,<br \/>\nP(-1, 2), Q(-1, 0), and R(2, 0)<br \/>\nRotation about the origin<br \/>\nP(-1, 2) = P'(1,-2)<br \/>\nQ(-1, 0) = Q'(1,0)<br \/>\nR(2, 0) = R'(-2,0)<br \/>\nHence the coordinate of the image is P'(1,-2), Q'(1,0), R'(-2,0)<br \/>\n<strong>Now reflecting above image point about x-axis:<\/strong><br \/>\nWhen a point is reflected about the x-axis then the y-coordinate becomes opposite.<br \/>\nA(x, y) = A'(x, -y)<br \/>\nGiven,<br \/>\nP'(1,-2), Q'(1,0), R'(-2,0)<br \/>\nRotation about the origin<br \/>\nP'(1,-2) = P&#8221;(1,2)<br \/>\nQ'(1,0) = Q&#8221;(1,0)<br \/>\nR'(-2,0) = R&#8221;(-2,0)<br \/>\nHence the coordinate of the image are P'(1,2), Q'(1,0), R'(-2,0)<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 7.<br \/>\n<strong>IDENTIFYING A ROTATION<\/strong><br \/>\nTell whether the blue \ufb01gure is a rotation of the red \ufb01gure about point P. If so, give the angle and direction of rotation.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33319\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-48.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 48\" width=\"172\" height=\"109\" \/><\/p>\n<p>Answer:<br \/>\nYes, the blue figure is the rotation of the red figure about the origin.<\/p>\n<p>Explanation:<br \/>\nBecause when we will rotate the red figure 90 degrees anti-clockwise about the origin we will get the same figure as the blue figure.<br \/>\nBy this, we can say that the blue figure is the result of the rotation of red figure by 90 degrees in the clock or anti-clockwise direction.<\/p>\n<p>Question 8.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nWhich is different? Find \u201cboth\u201d answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33320\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-49.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 49\" width=\"387\" height=\"253\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-49.png 387w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-49-300x196.png 300w\" sizes=\"(max-width: 387px) 100vw, 387px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33321\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-50.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 50\" width=\"195\" height=\"192\" \/><\/p>\n<p>Answer:<br \/>\nThe statement which different from all other 3 statement is:<br \/>\nWhat are the coordinates of the image after a 270 degrees clockwise rotation about the origin?<br \/>\nNow coordinate of both the image are:<br \/>\nThe rotation of an object 90 degrees clockwise is equal to the rotation of 270 degrees counterclockwise.<br \/>\nwe know that when a point is rotated 270 degrees counterclockwise about origin then both coordinate gets interchanges and x-coordinate becomes opposite.<br \/>\nA(x, y) = A'(y, -x)<br \/>\nGiven,<br \/>\nA(2, 4)<br \/>\nB(4, 4)<br \/>\nC(4, 1)<br \/>\nRotating 90 degrees clockwise about the origin<br \/>\nA(2,4) = A'(4,-2)<br \/>\nB(4, 4) = B'(4,-4)<br \/>\nC(4, 1) = C'(1,-4)<br \/>\nHence the coordinate of the image are: A'(4,-2), B'(4,-4), C'(1,-4)<br \/>\nImage of statement which different from all 3 statement<br \/>\nThe rotation of an object 270 degrees clockwise is equal to the rotation of 90 degrees counterclockwise.<br \/>\nwe know that when a point is rotated 90 degrees counterclockwise about origin then both coordinate gets interchanges and x-coordinate becomes opposite<br \/>\nP(x, y) = P'(-y, x)<br \/>\nGiven,<br \/>\nA(2, 4)<br \/>\nB(4, 4)<br \/>\nC(4, 1)<br \/>\nRotating 90 degrees clockwise about the origin<br \/>\nA(2, 4) = A'(-4, 2)<br \/>\nB(4, 4) = B'(-4, 4)<br \/>\nC(4, 1) = C'(-1, 4)<br \/>\nHence the coordinate of the image are: A'(4,-2), B'(-4,4), C'(-1,4)<br \/>\nThird statement &#8220;what are the coordinates of the image after a 270 degrees clockwise rotation about origin?&#8221; is different.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 9.<br \/>\nYou move the red game piece to the indicated location using a rotation about the origin, followed by a translation. What are the coordinates of the vertices of the game piece after the rotation? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33322\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-51.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations 51\" width=\"193\" height=\"193\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-51.png 193w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-51-150x150.png 150w\" sizes=\"(max-width: 193px) 100vw, 193px\" \/><\/p>\n<p>Answer:<br \/>\nTo move the red game piece in the indicated location the game piee should be rotated 90 degrees in clockwise direction. The rotation of red game piece 90 degrees clockwise is same as the rotation of 270 degrees counterclockwise.<br \/>\nwe know that when a point is rotated 270 degrees counterclockwise about origin then both coordinate gets interchanges and x-coordinate becomes opposite.<br \/>\nA(x,y) = A'(y, -x)<br \/>\nConner point of red game piece:<br \/>\nA(0,-1), B(0,0), C(1,0), D(1,1), E(-2,1), F(-2,0), G(-1,0), H(-1,-1)<br \/>\nRotating 90 degrees clockwise about the origin:<br \/>\nA(0,-1) = A'(-1,0)<br \/>\nB(0,0) = B'(0,0)<br \/>\nC(1,0) = C'(0,-1)<br \/>\nD(1,1) = D'(1,-1)<br \/>\nE(-2,1) = E'(1,2)<br \/>\nF(-2,0) = F'(0,2)<br \/>\nG(-1,0) = G'(0,1)<br \/>\nH(-1,-1) = H'(-1,1)<br \/>\nHence the coordinate of corner of red game piece are A'(-1,0), B'(0,0), C'(0,-1), D'(1,-1), E'(1,2), F'(0,2), G'(0,1), H'(-1,1)<\/p>\n<p>Question 10.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nSkytypingis a technique that airplanes use to write messages in the sky. The coordinate plane shows a message typed in the sky over a city, where the positive y-axis represents north. What does the message say? How can you transform the message so that it is read from north to south?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33323\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-52.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 52\" width=\"210\" height=\"120\" \/><\/p>\n<p>Answer: HELLO<\/p>\n<p>Explanation:<br \/>\nThe message above on the coordinate plane can be transformed from north to south by rotating the image 90 degrees anticlockwise.<\/p>\n<h3><a id=\"Rotations_Homework_&amp;_Practice_2.3\"><\/a>Rotations Homework &amp; Practice 2.3<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Tell whether the blue \ufb01gure is a re\ufb02ection of the red \ufb01gure.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33324\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-53.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 53\" width=\"147\" height=\"118\" \/><\/p>\n<p>Answer: Yes, the blue figure is the reflection of red figure.<\/p>\n<p>Explanation:<br \/>\nBecause the blue figure is the exact mirror image of the red figure. If the red figure will be flipped it will result in the blue figure. So, the blue figure is the reflection of red figure.<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33325\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-54.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 54\" width=\"155\" height=\"92\" \/><\/p>\n<p>Answer: No, the blue figure is not the reflection of red figure.<\/p>\n<p>Explanation:<br \/>\nBecause the blue figure is not the mirror image of the red figure. If the red figure will be flipped it will not result in the blue figure. So blue figure is not reflection of red figure.<\/p>\n<p>Find the circumference of the object. Use 3.14 or \\(\\frac{22}{7}\\) for \u03c0.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33326\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-55.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 55\" width=\"166\" height=\"127\" \/><\/p>\n<p>Answer:<br \/>\nGiven diameter of disk D = 28 cm<br \/>\nCircumference of the circular disk is \u03c0 \u00d7 D<br \/>\nC = \u03c0 \u00d7 28<br \/>\nC = 22\/7 \u00d7 28<br \/>\nC = 22 \u00d7 4<br \/>\nC = 88 cm<br \/>\nThus the circumference is 88 cm.<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33327\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-56.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 56\" width=\"168\" height=\"125\" \/><\/p>\n<p>Answer:<br \/>\nGiven the diameter of disk D = 11.4 in<br \/>\nCircumference of the circular disk is \u03c0 \u00d7 D<br \/>\nC = \u03c0 \u00d7 11.4<br \/>\nC = 22\/7 \u00d7 11.4<br \/>\nC = 3.14 \u00d7 11.4<br \/>\nC = 35.796 in<br \/>\nThus the circumference is 35.796 in<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33328\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-57.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 57\" width=\"119\" height=\"133\" \/><\/p>\n<p>Answer:<br \/>\nGiven diameter of disk r = 0.5 ft<br \/>\nCircumference of the circular disk is 2\u03c0 \u00d7 r<br \/>\nC = 2\u03c0 \u00d7 0.5<br \/>\nC = 6.28 \u00d7 0.5<br \/>\nC = 3.14 ft<br \/>\nThus the circumference is 3.14 ft<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><\/p>\n<p><strong>DESCRIBING RELATIONSHIPS<\/strong><br \/>\n<strong>Describe the relationship between the given point and the point (2, 7) in terms of rotations.<\/strong> (See Exploration 1, p. 55.)<\/p>\n<p>Question 6.<br \/>\nB(7, -2)<\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nA(7, 2) = B(7, -2)<br \/>\nHere we can see that after rotation x and y coordinate are interchanged and the y-coordinate is opposite. And we know that when a point is rotated 270 degrees counterclockwise about origin then both coordinates get interchanged and the x-coordinate becomes opposite.<br \/>\nP(x, y) = P'(y, -x)<br \/>\nHence the above rotation is 270 degrees counterclockwise about the origin.<\/p>\n<p>Question 7.<br \/>\nC(-7, 2)<\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nA(7, 2) = C(-7, 2)<br \/>\nHere we can see that after rotation x and y coordinate are interchanged and the y-coordinate is opposite. And we know that when a point is rotated 270 degrees counterclockwise about origin then both coordinate gets interchanged and x-coordinate becomes opposite.<br \/>\nP(x, y) = P'(-y, x)<br \/>\nHence the above rotation is 90 degrees counterclockwise about the origin.<\/p>\n<p>Question 8.<br \/>\nD(-2, -7)<\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nA(2, 7) = C(-2, -7)<br \/>\nHere we can see that after rotation x and y coordinate are interchanged and the y-coordinate is opposite. And we know that when a point is rotated 270 degrees counterclockwise about origin then both coordinate gets interchanged and x-coordinate becomes opposite.<br \/>\nP(x, y) = P'(-x, -y)<br \/>\nHence the above rotation is 180 degrees counterclockwise about the origin.<\/p>\n<p><strong>IDENTIFYING A ROTATION<\/strong><br \/>\n<strong>Tell whether the blue \ufb01gure is a rotation of the red \ufb01gure about the origin. If so, give the angle and direction of rotation.<\/strong><\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33329\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-58.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 58\" width=\"198\" height=\"189\" \/><\/p>\n<p>Answer: No the blue figure is not the rotation of the red figure.<\/p>\n<p>Explanation:<br \/>\nBecause if the blue triangle were the result of the rotation of the red triangle then the hypotenuse of the blue triangle should have been parallel to the x-axis. so, it is not the case of rotation.<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33330\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-59.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 59\" width=\"196\" height=\"186\" \/><\/p>\n<p>Answer: Yes, the blue figure is the result of the rotation of the red figure.<\/p>\n<p>Explanation:<br \/>\nBecause if the red figure is rotated 90 degrees in a counterclockwise direction it will result in a blue figure.<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33331\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-60.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 60\" width=\"198\" height=\"186\" \/><\/p>\n<p>Answer: Yes, the blue figure is the result of the rotation of the red figure.<\/p>\n<p>Explanation:<br \/>\nIf the red figure is rotated 180 degrees in counterclockwise or clockwise direction it will result in blue figure.<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33332\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-61.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 61\" width=\"200\" height=\"200\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-61.png 200w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-61-150x150.png 150w\" sizes=\"(max-width: 200px) 100vw, 200px\" \/><\/p>\n<p>Answer: Yes, the blue figure is the result of the rotation of the red figure.<\/p>\n<p>Explanation:<br \/>\nIf the red figure is rotated 90 degrees in a clockwise direction it will result in blue figure.<\/p>\n<p><strong>ROTATING A FIGURE<\/strong><br \/>\n<strong>The vertices of a \ufb01gure are given. Rotate the \ufb01gure as described. Find the coordinates of the image.<\/strong><\/p>\n<p>Question 13.<br \/>\nA(2, -2), B(4, -1), C(4, -3), D(2, -4)<br \/>\n90\u00b0 counterclockwise about the origin<\/p>\n<p>Answer:<br \/>\nWe know that when a point is rotated 90 degrees counterclockwise about the origin then both coordinates gets interchanged and y-coordinate becomes opposite.<br \/>\nP(x, y) = P'(-y, x)<br \/>\nGiven,<br \/>\nA(2, -2), B(4, -1), C(4, -3), D(2, -4)<br \/>\nRotating 90 degrees counterclockwise about the origin<br \/>\nA(2, -2) = A'(2,2)<br \/>\nB(4, -1) = B'(1,4)<br \/>\nC(4, -3) = C'(3,4)<br \/>\nD(2, -4) = D'(4,2)<br \/>\nHence the coordinates of the image are A'(2,2), B'(1,4), C'(3,4), D'(4,2)<\/p>\n<p>Question 14.<br \/>\nF(1, 2), G(3, 5), H(3, 2) 180\u00b0 about the origin<\/p>\n<p>Answer:<br \/>\nWe know that when a point is rotated 180 degrees counterclockwise or clockwise direction about the origin then both coordinates gets interchanged and y-coordinate becomes opposite.<br \/>\nP(x, y) = P'(-x, -y)<br \/>\nGiven,<br \/>\nF(1, 2), G(3, 5), H(3, 2)<br \/>\nRotating 180 degrees about the origin<br \/>\nF(1, 2) = F'(-1,-2)<br \/>\nG(3, 5) = G'(-3,-5)<br \/>\nH(3, 2) = H'(-3,-2)<br \/>\nHence the coordinates of the image are F'(-1,-2), G'(-3,-5), H'(-3,-2)<\/p>\n<p>Question 15.<br \/>\nJ(-4, 1), K(-2, 1), L(-4, -3)<br \/>\n90\u00b0 clockwise about the origin<\/p>\n<p>Answer:<br \/>\nThe rotation of an object 90 degrees clockwise is equal to the rotation of 270 degrees counterclockwise.<br \/>\nWe know that when a point is rotated 270 degrees counterclockwise about the origin then both coordinates gets interchanged and y-coordinate becomes opposite.<br \/>\nP(x, y) = P'(y, -x)<br \/>\nGiven,<br \/>\nJ(-4, 1), K(-2, 1), L(-4, -3)<br \/>\nRotating 90 degrees clockwise about the origin<br \/>\nJ(-4, 1) = J'(1,4)<br \/>\nK(-2, 1) = K'(1,2)<br \/>\nL(-4, -3) = L'(-3,4)<br \/>\nHence the coordinates of the image are J'(1,4), K'(1,2), L'(-3,4)<\/p>\n<p>Question 16.<br \/>\nP(-3, 4), Q(-1, 4), R(-2, 1), S(-4, 1)<br \/>\n270\u00b0 clockwise about the origin<\/p>\n<p>Answer:<br \/>\nThe rotation of an object 270 degrees clockwise is equal to the rotation of 90 degrees counterclockwise.<br \/>\nWe know that when a point is rotated 90 degrees counterclockwise about the origin then both coordinates gets interchanged and y-coordinate becomes opposite.<br \/>\nP(x, y) = P'(-y, x)<br \/>\nGiven,<br \/>\nP(-3, 4), Q(-1, 4), R(-2, 1), S(-4, 1)<br \/>\nRotating 90 degrees clockwise about the origin<br \/>\nP(-3, 4) = P'(-4,-3)<br \/>\nQ(-1, 4) = Q'(-4,-1)<br \/>\nR(-2, 1) = R'(-1,-2)<br \/>\nS(-4, 1) = S'(-1,-4)<br \/>\nHence the coordinates of the image are P'(-4,-3), Q'(-4,-1), R'(-1,-2), S'(-1,-4)<\/p>\n<p>Question 17.<br \/>\nW(-6, -2), X(-2, -2), Y(-2, -6), Z(-5, -6)<br \/>\n270\u00b0 counterclockwise about the origin<\/p>\n<p>Answer:<br \/>\nWe know that when a point is rotated 270 degrees counterclockwise about the origin then both coordinates gets interchanged and y-coordinate becomes opposite.<br \/>\nP(x, y) = P'(y, -x)<br \/>\nGiven,<br \/>\nW(-6, -2), X(-2, -2), Y(-2, -6), Z(-5, -6)<br \/>\nRotating 90 degrees clockwise about the origin<br \/>\nW(-6, -2) = W'(-2,6)<br \/>\nX(-2, -2) = X'(-2,2)<br \/>\nY(-2, -6) = Y'(-6,2)<br \/>\nZ(-5, -6) = Z'(-6,5)<br \/>\nHence the coordinates of the image are W'(-2,6), X'(-2,2), Y'(-6,2), Z'(-6,5)<\/p>\n<p>Question 18.<br \/>\nA(1, -1), B(5, -6), C(1, -6)<br \/>\n90\u00b0 counterclockwise about the origin<\/p>\n<p>Answer:<br \/>\nWe know that when a point is rotated 90 degrees counterclockwise about the origin then both coordinates gets interchanged and y-coordinate becomes opposite.<br \/>\nP(x, y) = P'(-y, x)<br \/>\nGiven,<br \/>\nA(1, -1), B(5, -6), C(1, -6)<br \/>\nRotating 90 degrees clockwise about the origin<br \/>\nA(1, -1) = A'(1,1)<br \/>\nB(5, -6) = B'(6,5)<br \/>\nC(1, -6) = C'(6,1)<br \/>\nHence the coordinates of the image are A'(1,1), B'(6,5), C'(6,1)<\/p>\n<p>Question 19.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nThe vertices of a triangle are A(4, 4), B(1, -2), and C(-3, 0). Your friend \ufb01nds the coordinates of the image after a rotation 90\u00b0 clockwise about the origin. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33334\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-62.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 62\" width=\"229\" height=\"118\" \/><\/p>\n<p>Answer:<br \/>\nWe know that when a point is rotated 270 degrees counterclockwise about the origin then both coordinates gets interchanged and y-coordinate becomes opposite.<br \/>\nP(x, y) = P'(y, -x)<br \/>\nGiven,<br \/>\nA(4, 4), B(1, -2), and C(-3, 0).<br \/>\nRotating 90 degrees clockwise about the origin<br \/>\nA(4, 4) = A'(4,-4)<br \/>\nB(1, -2) = B'(-2,-1)<br \/>\nC(-3,0) = C'(0,3)<br \/>\nHence the coordinates of the image are A'(4,-4), B'(-2,-1), C'(0,3)<br \/>\nBy this I can say that my friend is not correct.<\/p>\n<p>Question 20.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA game show contestant spins the prize wheel shown. The arrow remains in a \ufb01xed position while the wheel rotates. The wheel stops spinning, resulting in an image that is a rotation 270\u00b0 clockwise about the center of the wheel. What is the result?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33333\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-62.1.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 62.1\" width=\"182\" height=\"184\" \/><\/p>\n<p>Answer: Free spin<\/p>\n<p>Explanation:<br \/>\nThe arrow is located at 90 degrees in the counterclockwise direction of free spin. So when the wheel is rotated 270 degrees in a clockwise direction the arrow will be on the free spin column.<\/p>\n<p><strong>PATTERN<\/strong><br \/>\n<strong>A \ufb01gure has rotational symmetry if a rotation of 180\u00b0 or less produces an image that \ufb01ts exactly on the original \ufb01gure. Determine whether the \ufb01gure has rotational symmetry. Explain your reasoning.<\/strong><\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33335\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-63.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 63\" width=\"198\" height=\"224\" \/><\/p>\n<p>Answer: Yes the given \ufb01gure has rotational symmetry.<\/p>\n<p>Explanation:<br \/>\nThe given figure in the problem is rotated 120 degrees in any direction clockwise or counterclockwise then it will produce the same identical image. Since 120 degrees is less than 180 degrees so it will have rotational symmetry.<\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33336\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-64.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 64\" width=\"205\" height=\"218\" \/><\/p>\n<p>Answer: No the given \ufb01gure does not have rotational symmetry.<\/p>\n<p>Explanation:<br \/>\nThe given figure in the problem will produce the same identical image only when it is rotated 360 degrees. Since 360 degrees is greater than 180 degrees so it will not have rotational symmetry.<\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33337\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-65.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 65\" width=\"216\" height=\"212\" \/><\/p>\n<p>Answer: Yes the given \ufb01gure has rotational symmetry.<\/p>\n<p>Explanation:<br \/>\nThe given figure in the problem will produce the same identical image only when it is rotated 180 degrees. Since the maximum angle for rotational symmetry is 180 degrees so it will have rotational symmetry.<\/p>\n<p><strong>USING MORE THAN ONE TRANSFORMATION<\/strong><br \/>\n<strong>The vertices of a \ufb01gure are given. Find the coordinates of the image after the transformations given.<\/strong><\/p>\n<p>Question 24.<br \/>\nR(-7, -5), S(-1, -2), T(-1, -5)<br \/>\nRotate 90\u00b0 counterclockwise about the origin. Then translate 3 units left and 8 units up.<\/p>\n<p>Answer:<br \/>\nWe know that when a point is rotated 90 degrees counterclockwise about origin then both coordinates gets interchanges and y-coordinate becomes opposite.<br \/>\nP(x,y) = P'(-y,x)<br \/>\nGiven, R(-7, -5), S(-1, -2), T(-1, -5)<br \/>\nRotating 90 degrees counterclockwise about the origin<br \/>\nR(-7,-5) = R'(5,-7)<br \/>\nS(-1, -2) = S'(2,-1)<br \/>\nT(-1, -5) = T'(5,-1)<br \/>\nThe coordinate of the image are R'(5,-7), S'(2,-1), T'(5,-1)<br \/>\nWe know that to translate a figure &#8216;a&#8217; units horizontally and &#8216;b&#8217; units vertically in coordinate plane, &#8216;a&#8217; is added to x-coordinate and &#8216;b&#8217; is added to y-coordinate of the vertices.<br \/>\nA(x,y) = A'(x+a, y+b)<br \/>\nThe value a and b will be positive if shift is Right and Vertical Up and the value of a and b will be negative if shift is left and vertical Down.<br \/>\nGiven, R'(5,-7), S'(2,-1), T'(5,-1) and a = -3, b = 8<br \/>\nR'(5+a, -7+b) = R&#8221;(5-3, -7+8) = R&#8221;(2,1)<br \/>\nS'(2+a, -1+b) = R&#8221;(2-3, -1+8) = S&#8221;(-1,7)<br \/>\nR'(5+a, -1+b) = R&#8221;(5-3, -1+8) = T&#8221;(2,7)<br \/>\nThe coordinate of the image are R&#8221;(2,1), S&#8221;(-1,7), T&#8221;(2,7)<\/p>\n<p>Question 25.<br \/>\nJ(-4, 4), K(-3, 4), L(-1, 1), M(-4, 1) Re\ufb02ect in the x-axis, and then rotate 180\u00b0 about the origin.<\/p>\n<p>Answer:<br \/>\nWe know that when a point is reflected about x-axis then y-coordinate becomes opposite.<br \/>\nA(x, y) = A'(x, -y)<br \/>\nGiven J(-4, 4), K(-3, 4), L(-1, 1), M(-4, 1)<br \/>\nReflection about the x-axis:<br \/>\nJ(-4, 4) = J'(-4,-4)<br \/>\nK(-3, 4) = K'(-3,-4)<br \/>\nL(-1, 1) = L'(-1,-1)<br \/>\nM(-4, 1) = M'(-4,-1)<br \/>\nThe coordinate of the image are J'(-4,-4), K'(-3,-4), L'(-1,-1), M'(-4,-1)<br \/>\nNow rotating the above image 180 degrees about the origin.<br \/>\nWe know that when a point is reflected about x-axis then y-coordinate becomes opposite.<br \/>\nA(x, y) = A'(-x, -y)<br \/>\nJ'(-4,-4), K'(-3,-4), L'(-1,-1), M'(-4,-1)<br \/>\nRotating 180 degrees about the origin:<br \/>\nJ'(-4,-4) = J&#8221;(4,4)<br \/>\nK'(-3,-4) = K&#8221;(3,4)<br \/>\nL'(-1,-1) = L&#8221;(1,1)<br \/>\nM'(-4,-1) = M&#8221;(4,1)<br \/>\nThe coordinate of the image are J&#8221;(4,4), K&#8221;(3,4), L&#8221;(1,1), M&#8221;(4,1)<\/p>\n<p><strong>CRITICAL THINKING<\/strong><br \/>\n<strong>Describe two different sequences of transformations in which the blue \ufb01gure is the image of the red \ufb01gure.<\/strong><\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33338\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-66.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 66\" width=\"261\" height=\"248\" \/><\/p>\n<p>Answer:<br \/>\nTwo different ways of translating a red figure in to blue figure:<br \/>\n1. First rotate the red figure 90 degrees in the counterclockwise direction and then translate that image 5 units towards the left to get the blue figure.<br \/>\n2. First rotate the red figure 90 degrees in a clockwise direction and then translate that image 1 unit towards the Right and 5 units Up to get the blue figure.<\/p>\n<p>Question 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33339\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-67.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 67\" width=\"246\" height=\"250\" \/><\/p>\n<p>Answer:<br \/>\nTwo different ways of translating a red figure in to blue figure:<br \/>\n1. First rotate the red figure 90 degrees in the counterclockwise direction and then translate that image 1 unit towards the left and 1 Down to get the blue figure.<br \/>\n2. First rotate the image in the x-axis and then translate that image 4 units towards the left and 2 units Up to get the blue figure.<\/p>\n<p>Question 28.<br \/>\n<strong>REASONING<\/strong><br \/>\nA trapezoid has vertices A(-6, -2), B(-3, -2), C(-1, -4), and D(-6, -4).<br \/>\na. Rotate the trapezoid 180\u00b0 about the origin. What are the coordinates of the image?<\/p>\n<p>Answer:<br \/>\nA(x, y) = A'(-x, -y)<br \/>\nGiven,<br \/>\nA(-6, -2), B(-3, -2), C(-1, -4), and D(-6, -4).<br \/>\nRotating 180 degrees about the origin:<br \/>\nA(-6, -2) = A'(6,2)<br \/>\nB(-3, -2) = B'(3,2)<br \/>\nC(-1, -4) = C'(1,4)<br \/>\nD(-6, -4) = D'(6,4)<br \/>\nThe coordinates of the image of trapezoid vertices are A'(6,2), B'(3,2), C'(1,4), D'(6,4)<\/p>\n<p>b. Describe a way to obtain the same image without using rotations.<\/p>\n<p>Answer:<br \/>\nIn the above question, we can see that the coordinates of all the vertices of the trapezoid are negative and all the coordinates of the image vertices are positive. So there is another way to get the vertices of the image.<br \/>\nFirst, reflect the trapezoid in the x-axis and then in the y-axis or first reflect the trapezoid in the y-axis and then in the x-axis.<\/p>\n<p><strong>ROTATING A FIGURE<\/strong><br \/>\n<strong>The vertices of a \ufb01gure are given. Rotate the \ufb01gure as described. Find the coordinates of the image.<\/strong><\/p>\n<p>Question 29.<br \/>\nD(2, 1), E(2, -2), F(-1, 4)<br \/>\n90\u00b0 counterclockwise about vertex D<\/p>\n<p>Answer:<br \/>\nP(x, y) = P'(-(y &#8211; b) + a, (x -a) + b)<br \/>\nGiven,<br \/>\nD(2, 1), E(2, -2), F(-1, 4)<br \/>\n(a, b) = (2, 1)<br \/>\nRotation about the point D(2,1)<br \/>\nD(2, 1) = D'(2,1)<br \/>\nE(2, -2) = E'(-(-2-1) + 2, (2 &#8211; 2) + 1) = E'(5, 1)<br \/>\nF(-1, 4) = F'(-(4 &#8211; 1) + 2, (-1 &#8211; 2) + 1) = F'(-1, -2)<br \/>\nHence the coordinate of the image: D'(2,1), E'(5, 1), F'(-1, -2)<\/p>\n<p>Question 30.<br \/>\nL(-4, -3), M(-1, -1), N(2, -2)<br \/>\n180\u00b0 about vertex M<\/p>\n<p>Answer:<br \/>\nWhen a point is rotated 180 degrees counterclockwise about a given point (a, b) then its both x and y coordinate becomes opposite and &#8216;b&#8217; and &#8216;a&#8217; are subtracted from x and y coordinate respectively.<br \/>\nP(x, y) = P'(-(x &#8211; a) + b, -(y &#8211; b) + a)<br \/>\nGiven,<br \/>\nL(-4, -3), M(-1, -1), N(2, -2)<br \/>\nRotation about the point M(-1, -1):<br \/>\nL(-4, -3) = L'(-(-4 + 1) &#8211; 1, -(-3 + 1) &#8211; 1) = L'(2, 1)<br \/>\nM(-1, -1) = M'(-1, -1)<br \/>\nN(2, -2) = N'(-(2 + 1) &#8211; 1, -(-2 + 1) &#8211; 1) = N'(-4, 0)<br \/>\nHence the coordinate of the image are L'(2, 1), M'(-1, -1), N'(-4, 0)<\/p>\n<p>Question 31.<br \/>\nW(-5, 0), X(-1, 4), Y(3, -1), Z(0, -4)<br \/>\n270\u00b0 counterclockwise about vertex W<\/p>\n<p>Answer:<br \/>\nWhen a point is rotated 270 degrees counterclockwise about a given point (a, b) then its both x and y coordinate becomes opposite and &#8216;b&#8217; and &#8216;a&#8217; are subtracted from x and y coordinate respectively.<br \/>\nP(x, y) = P'(-(x &#8211; a) + b, -(y &#8211; b) + a)<br \/>\nGiven,<br \/>\nW(-5, 0), X(-1, 4), Y(3, -1), Z(0, -4)<br \/>\nRotation about the point W(-5, 0):<br \/>\nW(-5, 0) = W'(-5, 0)<br \/>\nX(-1, 4) = X'((4 &#8211; 0) &#8211; 5, -(-1 + 5) + 0) = X'(-1, -4)<br \/>\nY(3, -1) = Y'((-1 &#8211; 0) &#8211; 5, -(3 + 5) + 0) = Y'(-6, -8)<br \/>\nZ(0, -4) = Z'((-4 &#8211; 0) &#8211; 5, -(0 + 5) + 0) = Z'(-9, -5)<br \/>\nHence the coordinate of the image are W'(-5, 0), X'(-1, -4), Y'(-6, -8), Z'(-9, -5)<\/p>\n<p>Question 32.<br \/>\nD(-3, -4), E(-5, 2), F(1, -1), G(3, -7)<br \/>\n270\u00b0 clockwise about vertex E.<\/p>\n<p>Answer:<br \/>\nWhen a point is rotated 90 degrees counterclockwise about a given point (a, b) then its both x and y coordinate becomes opposite and &#8216;b&#8217; and &#8216;a&#8217; are subtracted from x and y coordinate respectively.<br \/>\nP(x, y) = P'(-(x &#8211; a) + b, -(y &#8211; b) + a)<br \/>\nGiven,<br \/>\nD(-3, -4), E(-5, 2), F(1, -1), G(3, -7)<br \/>\nRotation about the point E(-5, 2):<br \/>\nD(-3, -4) = D'(-(-4 &#8211; 2) &#8211; 5, -(-3 + 5) + 2) = D'(1, 4)<br \/>\nE(-5, 2) = E'(-5, 2)<br \/>\nF(1, -1) = F'(-(-1 &#8211; 2) &#8211; 5, (1 + 5) + 2) = F'(-2, 8)<br \/>\nG(3, -7) = G'(-(-7 &#8211; 2) &#8211; 5, (3 + 5) + 2) = G'(4, 10)<br \/>\nHence the coordinate of the image are D'(1, 4), E'(-5, 2), F'(-2, 8), G'(4, 10)<\/p>\n<p>Question 33.<br \/>\n<strong>LOGIC<\/strong><br \/>\nYou want to \ufb01nd the treasure located on the map at <img loading=\"lazy\" class=\"alignnone size-full wp-image-33342\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-68.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 68\" width=\"24\" height=\"25\" \/>. You are located at <img loading=\"lazy\" class=\"alignnone size-full wp-image-33345\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-69.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 69\" width=\"24\" height=\"26\" \/>. The following transformations will lead you to the treasure, but they are not in the correct order. Find the correct order. Use each transformation exactly once.<\/p>\n<ul>\n<li>Rotate 180\u00b0 about the origin.<\/li>\n<li>Re\ufb02ect in the y-axis.<\/li>\n<li>Rotate 90\u00b0 counterclockwise about the origin.<\/li>\n<li>Translate 1 unit right and 1 unit up.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-33341\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-68.1.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 68.1\" width=\"428\" height=\"322\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-68.1.png 428w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-68.1-300x226.png 300w\" sizes=\"(max-width: 428px) 100vw, 428px\" \/><\/p>\n<p>Answer:<br \/>\nThe correct order of transformation to get the treasure are:<\/p>\n<ul>\n<li>Rotate 180\u00b0 about the origin.<\/li>\n<li>Rotate 90\u00b0 counterclockwise about the origin.<\/li>\n<li>Re\ufb02ect in the y-axis.<\/li>\n<li>Translate 1 unit right and 1 unit up.<\/li>\n<\/ul>\n<p>Question 34.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou rotate a triangle 90\u00b0 counterclockwise about the origin. Then you translate its image 1 unit left and 2 units down. The vertices of the \ufb01nal image are (-5, 0), (-2, 2), and (-2, -1). What are the vertices of the original triangle?<\/p>\n<p>Answer:<br \/>\nWhen a point is rotated 90 degrees counterclockwise about a given point (a, b) then its both x and y coordinate becomes opposite.<br \/>\nLet the three vertices of the triangle be: (x1, y1), (x2, y2), (x3, y3)<br \/>\nP(x, y) = P'(-y, x)<br \/>\nRotating 90 degrees counterclockwise about the origin:<br \/>\nA(x1, y1) = A'(-y1, x1)<br \/>\nB(x2, y2) = B'(-y2, x2)<br \/>\nC(x3, y3) = C'(-y3, x3)<br \/>\nNow translating the image of the vertex for the final image<br \/>\nWe know that to translate a figure &#8216;a&#8217; units horizontally and &#8216;b&#8217; units vertically in the coordinate plane, &#8216;a&#8217; is added to x-coordinate and &#8216;b&#8217; is added to the y-coordinate of the vertices.<br \/>\nA(x, y) = A'(x + a, y + b)<br \/>\nGiven,<br \/>\nA'(-y1, x1), B'(-y2, x2), C'(-y3, x3) and a = -1, b = -2<br \/>\nA'(-y1 + a, x1 + b) = A&#8221;(-y1 &#8211; 1, x1 &#8211; 2)<br \/>\nB'(-y2 + a, x2 + b) = B&#8221;(-y2 &#8211; 1, x2 &#8211; 2)<br \/>\nC'(-y3 + a, x3 + b) = C&#8221;(-y3 &#8211; 1, x3 &#8211; 2)<br \/>\nThe given coordinate of vertex point of final image are: (-5, 0), (-2, 2) and (-2, -1)<br \/>\nNow comparing the coordinate of the final image<br \/>\n(-y1 &#8211; 1, x1 &#8211; 2) = (-5, 0) so y1 = 4 and x1 = 2<br \/>\n(-y2 &#8211; 1, x2 &#8211; 2) = (-2, 2) so y2 = 1 and x2 = 4<br \/>\n(-y3 &#8211; 1, x3 &#8211; 2) = (-2, 1) so y3 = 1 and x3 = 1<br \/>\nHence the vertices of original triangle are (2, 4), (4, 1) and (1, 1)<\/p>\n<h3><a id=\"Lesson_2.4_Congruent_Figures\"><\/a>Lesson 2.4 Congruent Figures<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p><strong>Work with a partner.<\/strong><br \/>\na. For each pair of \ufb01gures whose vertices are given below, draw the \ufb01gures in a coordinate plane. Then copy one of the \ufb01gures onto a piece of transparent paper. Use transformations to try to obtain one of the \ufb01gures from the other \ufb01gure.<\/p>\n<ul>\n<li>A(-5, 1), B(-5, -4), C(-2, -4) and D(1, 4), E(1, -1), F(-2, -1)<\/li>\n<li>G(1, 2), H(2, -6), J(5, 0) and L(-1, -2), M(-2, 6), N(-5, 0)<\/li>\n<li>P(0, 0), Q(2, 2), R(4, -2) and X(0, 0), Y(3, 3), Z(6, -3)<\/li>\n<li>A(0, 4), B(3, 8), C(6, 4), D(3, 0) and<br \/>\nF(-4, -3), G(-8, 0), H(-4, 3), J(0, 0)<\/li>\n<li>P(-2, 1), Q(-1, -2), R(1, -2), S(1, 1) and<br \/>\nW(7, 1), X(5, -2), Y(3, -2), Z(3, 1)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-33343\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-69.1.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 69.1\" width=\"217\" height=\"239\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33344\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-69.2.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 69.2\" width=\"158\" height=\"240\" \/><br \/>\nb. Which pairs of \ufb01gures in part(a) are identical? Explain your reasoning.<br \/>\nc. FigureA and FigureB are identical. Do you think there must be a sequence of transformations that obtains Figure A from Figure B? Explain your reasoning.<\/p>\n<p><strong>2.4 Lesson<\/strong><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 1.<br \/>\nA triangle has vertices X(0, 4), Y(4, 4), and Z(4, 2). Is \u25b3XYZ congruent to any of the triangles in Example 1? Explain.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-49541\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-transformation-key-img_22-300x258.png\" alt=\"Big Ideas Math Grade 8 Chapter 2 transformation key img_22\" width=\"300\" height=\"258\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-transformation-key-img_22-300x258.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-transformation-key-img_22.png 498w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nAfter plotting the triangle XYZ on the coordinate plane we can say that the triangle XYZ is congruent to triangle PQR among all the given triangle in the figure. In fact, if triangle PQR is rotated 90 degrees clockwise of 270 degrees counterclockwise it will result in the triangle XYZ.<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 2.<br \/>\nDescribing a different Sequence of rigid motions between the figures.<\/p>\n<p>Answer:<br \/>\nDifferent sequence of rigid motion to get the blue figure from the red figure are:<br \/>\n1. First rotate the red figure 90 degrees clockwise and the origin.<br \/>\n2. Then translate the image 4 units Right and 1 unit Up.<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 3.<br \/>\n<strong>IDENTIFYING CONGRUENT FIGURES<\/strong><br \/>\nUse the coordinate plane shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33346\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-70.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 70\" width=\"189\" height=\"190\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-70.png 189w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-70-150x150.png 150w\" sizes=\"(max-width: 189px) 100vw, 189px\" \/><br \/>\na. Identify any congruent \ufb01gures.<\/p>\n<p>Answer: a. After seeing the figure we can say that triangle ABCD is congruent to triangle JKLM.<\/p>\n<p>b. A rectangle has vertices W(4, 1), X(4, 2), Y(1, 2), and Z(-1, -1). Is Rectangle WXYZ congruent to any of the rectangles in the coordinate plane? Explain.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-49543\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-Grade-8-ch-2-solution-key-img_23-300x298.png\" alt=\"Big ideas math Grade 8 ch 2 solution key img_23\" width=\"300\" height=\"298\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-Grade-8-ch-2-solution-key-img_23-300x298.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-Grade-8-ch-2-solution-key-img_23-150x150.png 150w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-Grade-8-ch-2-solution-key-img_23.png 364w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nRectangle WXYZ is not congruent to any of the rectangles in the given figure because rectangle WXYZ is square of 3 units sides and the other rectangle in the figure does not have all the sides of 3 units.<\/p>\n<p><strong>RIGID MOTIONS<\/strong><br \/>\n<strong>The red \ufb01gure is congruent to the blue \ufb01gure. Describe a sequence of rigid motions between the \ufb01gures.<\/strong><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33347\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-71.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 71\" width=\"195\" height=\"190\" \/><\/p>\n<p>Answer:<br \/>\nThe sequence of the rigid motions from the red-figure to the blue figure:<br \/>\n1. First we will rotate the red figure 180 degrees clockwise or anticlockwise about the origin because the given red figure in the 4th quadrant and the blue figure is in the 2nd quadrant.<br \/>\n2. Then we will translate the image 1 unit left because one vertex (-1,-4) of red figure is on the negative side of the x-axis.<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33348\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-72.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 72\" width=\"199\" height=\"190\" \/><\/p>\n<p>Answer:<br \/>\nThe sequence of the rigid motions from red figure to blue figure:<br \/>\n1. First we will rotate the red figure 90 degrees clockwise about the origin because the given red figure in the 1st quadrant.<br \/>\n2. Then we will translate the image 3 units right and 1 unit down.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 6.<br \/>\nIn the coordinate plane at the left, each grid line represents 50 feet. Each \ufb01gure represents a pasture.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33349\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-73.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 73\" width=\"189\" height=\"198\" \/><br \/>\na. Are the \ufb01gures congruent? Use rigid motions to justify your answer.<\/p>\n<p>Answer: No the blue figure and red figure are not congruent.<\/p>\n<p>Explanation:<br \/>\nBy reflecting the red figure about the y-axis and translating the image 4 units Up we will not the same blue figure. So both figure are not congruent to each other.<\/p>\n<p>b. How many feet of fencing do you need to enclose each pasture?<\/p>\n<p>Answer:<br \/>\nGiven the length of each grid line = 50 feet<br \/>\nTotal feet of fencing = 50 \u00d7 total number of grid line along the boundary<br \/>\nFor red figure fencing: 50 \u00d7 12 = 600 feet<br \/>\nFor blue figure fencing: 50 \u00d7 12 = 600 feet<\/p>\n<p>Question 7.<br \/>\nA home decorator uses a computer to design a \ufb02oor tile. How can the decorator transform the tile as shown?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33350\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-74.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 74\" width=\"214\" height=\"128\" \/><\/p>\n<p>Answer:<br \/>\nFirst, rotate the given tiles about 90 degrees in the clockwise direction and then take the mirror image about the vertical axis.<\/p>\n<h3><a id=\"Congruent_Figures_Homework_&amp;_Practice_2.4\"><\/a>Congruent Figures Homework &amp; Practice 2.4<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>The vertices of a \ufb01gure are given. Rotate the \ufb01gure as described. Find the coordinates of the image.<\/strong><\/p>\n<p>Question 1.<br \/>\nA(1, 3), B(2, 5), C(3, 5), D(2, 3)<br \/>\n90\u00b0 counterclockwise about the origin<\/p>\n<p>Answer:<br \/>\nWhen a point is rotated 90 degrees about the origin then both x and y-coordinates become opposite.<br \/>\nA(x, y) = A'(-y, x)<br \/>\nGiven,<br \/>\nA(1, 3), B(2, 5), C(3, 5), D(2, 3)<br \/>\nRotating 90 degrees counterclockwise about the origin:<br \/>\nA(1, 3) = A'(-3, 1)<br \/>\nB(2, 5) = B'(-5, 2)<br \/>\nC(3, 5) = C'(-5, 3)<br \/>\nD(2, 3) = D'(-3, 2)<br \/>\nHence the coordinate of the image are A'(-3, 1), B'(-5, 2), C'(-5, 3), D'(-3, 2)<\/p>\n<p>Question 2.<br \/>\nF(-2, 1), G(-1, 3), H(3, 1)<br \/>\n180\u00b0 about the origin<\/p>\n<p>Answer:<br \/>\nWhen a point is rotated 180 degrees about the origin then both x and y-coordinates become opposite.<br \/>\nA(x, y) = A'(-x, -y)<br \/>\nGiven,<br \/>\nF(-2, 1), G(-1, 3), H(3, 1)<br \/>\nRotating 90 degrees counterclockwise about the origin:<br \/>\nF(-2, 1) = F'(2,-1)<br \/>\nG(-1, 3) = G'(1,-3)<br \/>\nH(3, 1) = H'(-3,-1)<br \/>\nHence the coordinate of the image are F'(2,-1), G'(1,-3), H'(-3,-1)<\/p>\n<p><strong>Factor the expression using the greatest common factor.<\/strong><\/p>\n<p>Question 3.<br \/>\n4n &#8211; 32<\/p>\n<p>Answer:<br \/>\n4n &#8211; 32<br \/>\nTake 4 as a common factor.<br \/>\n4(n &#8211; 8)<br \/>\nThus the greatest common factor is 4(n &#8211; 8)<\/p>\n<p>Question 4.<br \/>\n3w + 66<\/p>\n<p>Answer:<br \/>\n3w + 66<br \/>\nTake 3 as a common factor.<br \/>\n3(w + 22)<br \/>\nThus the greatest common factor is 3(w + 22)<\/p>\n<p>Question 5.<br \/>\n2y &#8211; 18<\/p>\n<p>Answer:<br \/>\n2y &#8211; 18<br \/>\nTake 2 as a common factor.<br \/>\n2(y &#8211; 9)<br \/>\nThus the greatest common factor is 2(y &#8211; 9).<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><br \/>\n<strong>TRANSFORMING FIGURES<\/strong><br \/>\n<strong>The vertices of a pair of \ufb01gures are given. Determine whether the \ufb01gures are identical.<\/strong> (See Exploration 1, p. 63.)<\/p>\n<p>Question 6.<br \/>\nG(0, 0), H(3, 2), J(1, -2) and L(-1, 0), M(2, 2), N(0, -3)<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-49548\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Solution-Key-Chapter-2-img_24-300x300.png\" alt=\"Big Ideas Math 8th Grade Solution Key Chapter 2 img_24\" width=\"300\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Solution-Key-Chapter-2-img_24-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Solution-Key-Chapter-2-img_24-150x150.png 150w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Solution-Key-Chapter-2-img_24.png 540w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nAfter plotting the triangles GHJ and LMN we can say that the triangle LMN are bigger compared to the other triangle. Thus both the triangles are not identical.<\/p>\n<p>Question 7.<br \/>\nA(-2, -1), B(-2, 2), C(-1, 1), D(-1, -2) and F(-2, 0), G(-1, 1), H(2, 1), J(1, 0)<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-49551\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Answer-Key-for-BIM-Grade-8-Chapter-2-tranformations-img_25-300x260.png\" alt=\"Answer Key for BIM Grade 8 Chapter 2 tranformations img_25\" width=\"300\" height=\"260\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Answer-Key-for-BIM-Grade-8-Chapter-2-tranformations-img_25-300x260.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Answer-Key-for-BIM-Grade-8-Chapter-2-tranformations-img_25.png 560w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nBy seeing both the quadrilaterals ABCD and FGHJ we can say that they are identical.<\/p>\n<p><strong>IDENTIFYING CONGRUENT FIGURES<\/strong><br \/>\n<strong>Identify any congruent \ufb01gures in the coordinate plane.<\/strong><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33351\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-75.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 75\" width=\"196\" height=\"189\" \/><\/p>\n<p>Answer:<br \/>\nOn observing the diagram in the given figure we can see that the shape and size of pentagon ABCDE and pentagon FKJHG are the same. The length of each side of both the pentagon is the same. Thus they are congruent.<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33352\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-76.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 76\" width=\"197\" height=\"191\" \/><\/p>\n<p>Answer:<br \/>\nBy seeing the above figure we can say that the shape and size of parallelogram EFGH and parallelogram BCDA are the same. The length of each side of both the parallelogram are same. Parallelogram BCDA can be obtained by rotating parallelogram EFGH 90 degrees clockwise and translating its image. Hence the parallelogram, EFGH is congruent to BCDA.<\/p>\n<p><strong>DESCRIBING A SEQUENCE OF RIGID MOTIONS<\/strong><br \/>\n<strong>The red \ufb01gure is congruent to the blue \ufb01gure. Describe a sequence of rigid motions between the \ufb01gures.<\/strong><\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33353\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-77.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 77\" width=\"196\" height=\"188\" \/><\/p>\n<p>Answer:<br \/>\nThe sequence of rigid motions between the red and blue figures are:<br \/>\n1. First we will rotate the red figure 90 degrees clockwise about the origin because the given red figure is in the 2nd quadrant and the blue figure is in the 1st quadrant.<br \/>\n2. Then we will translate the image 1 unit left and 1 unit Down because one vertex of the red figure is at (-1, 1)<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33354\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-78.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 78\" width=\"196\" height=\"191\" \/><\/p>\n<p>Answer:<br \/>\nThe sequence of rigid motions between the red and blue figures are:<br \/>\n1. First we will rotate the red figure 180 degrees clockwise or anticlockwise about the origin because the given red figure is in 4th quadrant and the blue figure is in the 2nd quadrant.<br \/>\n2. Then we will translate the image 1 unit Right and 1 unit Down because one vertex of red figure is at (2, -2)<\/p>\n<p>Question 12.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend describes a sequence of rigid motions between the \ufb01gures. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33355\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-79.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 79\" width=\"448\" height=\"198\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-79.png 448w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-79-300x133.png 300w\" sizes=\"(max-width: 448px) 100vw, 448px\" \/><\/p>\n<p>Answer:<br \/>\nWhen a point is reflected about x-axis then the y-coordinate becomes opposite.<br \/>\nA(x, y) = A'(x, -y)<br \/>\nCoordinates of red figure are A(1, -1), B(3, -1), C(4, -3), D(2, -3)<br \/>\nReflection about the x-axis:<br \/>\nA(1, -1) = A'(1, 1)<br \/>\nB(3, -1) = B'(3, 1)<br \/>\nC(4, -3) = C'(4, 3)<br \/>\nD(2, -3) = D'(2, 3)<br \/>\nNow translating the above image point 5 unit left.<br \/>\nCoordinate of the vertex of blue figure are: A&#8221;(-4, 1), B&#8221;(3,1), C&#8221;(-1, 3), D&#8221;(-3,3)<br \/>\nWe know that to translate a figure &#8216;a&#8217; units horizontally and &#8216;b&#8217; units vertically in coordinate plane, &#8216;a&#8217; is added to x-coordinate and &#8216;b&#8217; is added to y-coordinate of the vertices.<br \/>\nA(x,y) = A'(x+a, y+b)<br \/>\nThe value a and b will be positive if the shift is Right and Vertical Up and the value of a and b will be negative if the shift is left and vertical Down.<br \/>\nGiven:<br \/>\nA(1, 1), B(3, 1), C(4, 3), D(2, 3) and a = -5, b = 0<br \/>\nA&#8221;(1+a, 1+b) = A&#8221;(1-5, 1+0) = A&#8221;(-4, 1)<br \/>\nB&#8221;(3+a, 1+b) = B&#8221;(3-5, 1+0) = B&#8221;(-2,1)<br \/>\nC&#8221;(4+a,3+b) = C&#8221;(4-5, 3+0) = C&#8221;(-1, 3)<br \/>\nD&#8221;(2+a,3+b) = D&#8221;(2-5, 3+0) = D&#8221;(-3,3)<br \/>\nHence the coordinate of image are A&#8221;(-4, 1), B&#8221;(-2,1), C&#8221;(-1, 3), D&#8221;(-3,3)<br \/>\nSince the coordinate of the vertex of the blue is the same in both ways.<br \/>\nWe can say that the blue figure is obtained by the rigid motion of the red figure.<\/p>\n<p><strong>NAMING CORRESPONDING PARTS<\/strong><br \/>\n<strong>The \ufb01gures are congruent. Name the corresponding angles and the corresponding sides.<\/strong><\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33356\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-80.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 80\" width=\"220\" height=\"141\" \/><\/p>\n<p>Answer:<br \/>\nCorresponding sides of the congruent figure are<br \/>\nAD = EH<br \/>\nAB = EF<br \/>\nBC = FG<br \/>\nCD = GH<br \/>\nCorresponding angles of the congruent figure are<br \/>\n\u2220A = \u2220E<br \/>\n\u2220B = \u2220F<br \/>\n\u2220C = \u2220G<br \/>\n\u2220D = \u2220H<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33357\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-81.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 81\" width=\"285\" height=\"141\" \/><\/p>\n<p>Answer:<br \/>\nCorresponding sides of the congruent figure are<br \/>\nPQ = WV<br \/>\nQR = VZ<br \/>\nRS = ZY<br \/>\nST = YX<br \/>\nTP = XW<br \/>\nCorresponding angles of the congruent figure are<br \/>\n\u2220P = \u2220W<br \/>\n\u2220Q = \u2220V<br \/>\n\u2220R = \u2220Z<br \/>\n\u2220S = \u2220Y<br \/>\n\u2220T = \u2220X<\/p>\n<p>Question 15.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou use a computer program to transform an emoji. How can you transform the emoji as shown?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33358\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-82.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 82\" width=\"207\" height=\"117\" \/><\/p>\n<p>Answer:<br \/>\nFirst, take the reflection of that emoji about vertical line and then rotate that image 90 degrees clockwise to get that given emoji.<\/p>\n<p>Question 16.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nTwo \ufb01gures are congruent. Are the areas of the two \ufb01gures the same? the perimeters? Explain your reasoning.<\/p>\n<p>Answer:<\/p>\n<ul>\n<li>The size of both figures should be the same.<\/li>\n<li>The shape of both the figures should be the same.<\/li>\n<li>All the corresponding angles should be the same.<\/li>\n<li>Both the area and perimeter of two congruent figures are the same.<\/li>\n<\/ul>\n<p>Question 17.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe houses are identical.<br \/>\na. What is the length of side LM?<\/p>\n<p>Answer:<br \/>\nLength of LM = length of CD<br \/>\nlength of CD = 32 feet<br \/>\nSo, the length of LM is 32 feet<\/p>\n<p>b.Which angle of JKLMN corresponds to \u2220D?<br \/>\nAnswer:<br \/>\n\u2220D = \u2220M<br \/>\nThus \u2220M corresponds to \u2220D<\/p>\n<p>c. Side AB is congruent to side AE. What is the length of side AB? What is the perimeter of ABCDE?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33359\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-83.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 83\" width=\"344\" height=\"152\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-83.png 344w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-83-300x133.png 300w\" sizes=\"(max-width: 344px) 100vw, 344px\" \/>.<\/p>\n<p>Answer:<br \/>\nAE = JN<br \/>\nThe length of JN is 20 ft<br \/>\nSo, the length of AE = 20 ft<br \/>\nPerimeter of ABCDE = AB + BC + CD + DE + EA<br \/>\nPerimeter of ABCDE = 20 + 12 + 32 + 12 + 20 = 96 feet<br \/>\nThus the Perimeter of ABCDE\u00a0 is 96 feet<\/p>\n<p>Question 18.<br \/>\n<strong>REASONING<\/strong><br \/>\nTwo constellations are represented by the \ufb01gures in the coordinate plane shown. Are the \ufb01gures congruent? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33360\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-84.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 84\" width=\"349\" height=\"192\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-84.png 349w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-84-300x165.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/><\/p>\n<p>Answer:<br \/>\nThe above figure can be tranformed into below figure by rotating the figure 180 degrees clockwise or counterclockwise about the origin and translating the image 8 units Right and 8 units Up to get the above figure.<\/p>\n<h3><a id=\"Lesson_2.5_Dilations\"><\/a>Lesson 2.5 Dilations<\/h3>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-33361\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-85.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 85\" width=\"525\" height=\"177\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-85.png 525w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-85-300x101.png 300w\" sizes=\"(max-width: 525px) 100vw, 525px\" \/><\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p><strong>Work with a partner. Use geometry software.<\/strong><br \/>\na. Draw a polygon in the coordinate plane. Then dilate the polygon with respect to the origin. Describe the scale factor of the image.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33363\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-86.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 86\" width=\"160\" height=\"190\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33362\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-86.1.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 86.1\" width=\"401\" height=\"274\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-86.1.png 401w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-86.1-300x205.png 300w\" sizes=\"(max-width: 401px) 100vw, 401px\" \/><br \/>\nb. Compare the image and the original polygon in part(a). What do you notice about the sides? the angles?<br \/>\nc. Describe the relationship between each point below and the point A(x, y) in terms of dilations.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33364\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-87.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 87\" width=\"412\" height=\"43\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-87.png 412w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-87-300x31.png 300w\" sizes=\"(max-width: 412px) 100vw, 412px\" \/><br \/>\nd. What are the coordinates of a point P(x, y) after a dilation with respect to the origin by a scale factor of k?<\/p>\n<p><strong>2.5 Lesson<\/strong><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Tell whether the blue \ufb01gure is a dilation of the red \ufb01gure.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33365\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-88.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 88\" width=\"182\" height=\"73\" \/><\/p>\n<p>Answer:<br \/>\nNo the blue \ufb01gure is not the dilation of the red \ufb01gure.<\/p>\n<p>Explanation:<br \/>\nBlue and red figure has same size and same shape but the blue figure is reflection about vertical axis. So, the lines corresponding vertices of both figure does not meet at a point. This means that the blue figure is not the dilation of the red figure.<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33366\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-89.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 89\" width=\"147\" height=\"95\" \/><\/p>\n<p>Answer: Yes, the blue \ufb01gure is a dilation of the red \ufb01gure.<\/p>\n<p>Explanation:<br \/>\nWe observe that all the angles of red figure are congruent to the angles of red figure. Also their will be lines connecting the corresponding verrtices meeting at a point. This means that blue figure is dilation of the red figure.<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 3.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nTriangle ABC is dilated by a scale factor of 2. What are the coordinates of the image?<\/p>\n<p>Answer:<br \/>\nWhen the points of given figure are dilated we simply multiply each x and y coordinate by the given scale factor.<br \/>\nP(x, y) = P'(x . a, y . a)<br \/>\nGiven points of the triangle: A (1, 3), B (2, 3), C (2, 1) and scale factor = 2<br \/>\nDilating the figure by scale factor of 2<br \/>\nA (1, 3) = A'(1 . 2, 3 . 2) = A'(2, 6)<br \/>\nB (2, 3) = B'(2 . 2, 3 . 2) = B'(4, 6)<br \/>\nC (2, 1) = C'(2 . 2, 1 . 2) =\u00a0 C'(4, 2)<br \/>\nHence the coordinates of the image are A'(2, 6), B'(4, 6),\u00a0 C'(4, 2)<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 4.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nRectangle WXYZ is dilated by a scale factor of \\(\\frac{1}{4}\\). What are the coordinates of the image?<\/p>\n<p>Answer:<br \/>\nWhen the points of given figure are dilated we simply multiply each x and y coordinate by the given scale factor.<br \/>\nP(x, y) = P'(x . a, y . a)<br \/>\nGiven points of the rectangle: W(-4, -6), X(-4, 8), Y(4, 8), Z(4, -6)<br \/>\nscale factor = 0.25<br \/>\nW(-4, -6) = W'(-4 \u00d7 0.25, -6 \u00d7 0.25) = W'(-1, -1.5)<br \/>\nX(-4, 8) = X'(-4 \u00d7 0.25, 8 \u00d7 0.25) = X'(-1, 2)<br \/>\nY(4, 8) = Y'(4 \u00d7 0.25, 8 \u00d7 0.25) = Y'(1, 2)<br \/>\nZ(4, -6) = Z'(4 \u00d7 0.25, -6 \u00d7 0.25) = Z'(1, -1.5)<br \/>\nHence the coordinates of the image are W'(-1, -1.5), X'(-1, 2), Y'(1, 2), Z'(1, -1.5)<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 5.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nTrapezoid ABCDis dilated using a scale factor of 3, and then rotated 180\u00b0 about the origin. What are the coordinates of the image?<\/p>\n<p>Answer:<br \/>\nWhen the points of given figure are dilated we simply multiply each x and y coordinate by the given scale factor.<br \/>\nP(x, y) = P'(x . a, y . a)<br \/>\na is the scaling factor<br \/>\nGiven points of trapezoid: A(-2, -1), B(-1,1), C(0,1), D(0,-1) scale factor = 3<br \/>\nDilating the figure by scale factor of 3<br \/>\nA(-2, 1) = A'(-2 . 3, -1 . 3) = A'(-6, -3)<br \/>\nB(-1, 1) = B'(-1 . 3, 1 . 3) = B'(-3, 3)<br \/>\nC(0, 1) = C'(0 . 3, 1 . 3) = C'(0, 3)<br \/>\nD(0, -1) = D'(0 . 3, -1 . 3) = D'(0, -3)<br \/>\nThus the coodrinate of the image are A'(-6, -3), B'(-3, 3), C'(0, 3), D'(0, -3)<br \/>\nwhen a point is rotated 180 degrees about the origin then both x and y coordinate becomes opposite.<br \/>\nP(x, y) = P'(-x, -y)<br \/>\nImage points: A'(-6, -3), B'(-3, 3), C'(0, 3), D'(0, -3)<br \/>\nRotating 180 degrees about the origin:<br \/>\nA'(-6, -3) = A&#8221;(6, 3)<br \/>\nB'(-3, 3) = B&#8221;(3, -3)<br \/>\nC'(0, 3) = C&#8221;(0, -3)<br \/>\nD'(0, -3) = D&#8221;(0, 3)<br \/>\nThus the coodrinate of the image are A&#8221;(6, 3), B&#8221;(3, -3), C&#8221;(0, -3), D&#8221;(0, 3)<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><strong>IDENTIFYING A DILATION<\/strong><br \/>\n<strong>Tell whether the blue \ufb01gure is a dilation of the red \ufb01gure.<\/strong><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33367\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-90.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 90\" width=\"222\" height=\"99\" \/><\/p>\n<p>Answer: Yes, the blue \ufb01gure is a dilation of the red \ufb01gure.<\/p>\n<p>Explanation:<br \/>\nWe observe that all the angles of red figure are congruent to the angles of red figure. Also their will be lines connecting the corresponding vertices meeting at a point. This means that blue figure is dilation of the red figure.<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33368\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-91.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 91\" width=\"203\" height=\"119\" \/><\/p>\n<p>Answer: No the blue \ufb01gure is not the dilation of the red \ufb01gure.<\/p>\n<p>Explanation:<br \/>\nBlue and red figure has same size and same shape but the blue figure is reflection about vertical axis. So, the lines corresponding vertices of both figure does not meet at a point. This means that the blue figure is not the dilation of the red figure.<\/p>\n<p>Question 8.<br \/>\n<strong>DILATING A FIGURE<\/strong><br \/>\nThe vertices of a rectangle are J(4, 8), K(12, 8), L(12, 4), and M(4, 4). Draw the image after a dilation with a scale factor of \\(\\frac{1}{4}\\). Identify the type of dilation.<\/p>\n<p>Answer:<br \/>\nWhen the points of given figure are dilated we simply multiply each x and y coordinate by the given scale factor.<br \/>\nP(x, y) = P'(x . a, y . a)<br \/>\na is scale factor<br \/>\nGiven, vertices of a rectangle are J(4, 8), K(12, 8), L(12, 4), and M(4, 4), scale factor = 0.25<br \/>\nJ(4, 8) = J'(4 \u00d7 0.25, 8 \u00d7 0.25) = J'(1, 2)<br \/>\nK(12, 8) = K'(12 \u00d7 0.25, 8 \u00d7 0.25) = K'(3, 2)<br \/>\nL(12, 4) = L'(12 \u00d7 0.25, 4 \u00d7 0.25) = L'(3, 1)<br \/>\nM(4, 4) = M'(4 \u00d7 0.25, 4 \u00d7 0.25) = M'(1, 1)<br \/>\nHence the coordinates of the image are J'(1, 2), K'(3, 2), L'(3, 1), M'(1, 1)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-49588\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-img_26-300x201.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations img_26\" width=\"300\" height=\"201\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-img_26-300x201.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-img_26.png 752w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 9.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nHow is a dilation different from other transformations?<\/p>\n<p>Answer:<br \/>\nThe difference between dilation and other transformations are<\/p>\n<ul>\n<li>In the case of dilate the size of the figure after the dilation either decrease or increase but the shape of the figure before and after dilation remains same. Also after the dilation the corresponding angles will be congruent.<\/li>\n<li>In case of other transformations such as Rotation, translation, reflection the shape and size of figure before and after transformation remains the same.<\/li>\n<\/ul>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 10.<br \/>\nA photograph is dilated to \ufb01t in a frame, so that its area after the dilation is 9 times greater than the area of the original photograph. What is the scale factor of the dilation? Explain.<\/p>\n<p>Answer: The scale factor of length and breadth will be 3.<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nThe area after the dilation is 9 times greater than the area of the original photograph.<br \/>\nArea = length \u00d7 breadth<br \/>\np = 3 \u00d7 3<br \/>\nHence the scale factor of length and breadth will be 3.<\/p>\n<p>Question 11.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe location of a water treatment plant is mapped using a coordinate plane, where each unit represents 1 foot. The plant has vertices (0, 0), (0, 180), (240, 180), and (240, 0). You dilate the \ufb01gure with a scale factor of \\(\\frac{1}{3}\\). What are the coordinates of the image? What do you need to change so that the image accurately represents the location of the plant? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33369\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-92.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 92\" width=\"207\" height=\"256\" \/><\/p>\n<p>Answer:<br \/>\nWhen the points of given figure are dilated we simply multiply each x and y coordinate by the given scale factor.<br \/>\nP(x, y) = P'(x . a, y . a)<br \/>\na is the scaling factor<br \/>\nLocation of water treatment plant: A(0, 0), B(0, 180), C(240, 180), D(240, 0)<br \/>\nscale factor = \\(\\frac{1}{3}\\)<br \/>\nDilating the figure by scale factor of \\(\\frac{1}{3}\\)<br \/>\nA(0, 0) = A'(0 \u00d7 \\(\\frac{1}{3}\\), 0 \u00d7 \\(\\frac{1}{3}\\)) = A'(0, 0)<br \/>\nB(0, 180) = B'(0 \u00d7 \\(\\frac{1}{3}\\), 180 \u00d7 \\(\\frac{1}{3}\\)) = B'(0, 60)<br \/>\nC(240, 180) = C'(240 \u00d7 \\(\\frac{1}{3}\\), 180 \u00d7 \\(\\frac{1}{3}\\)) = C'(80, 60)<br \/>\nD(240, 0) = D'(240 \u00d7 \\(\\frac{1}{3}\\), 0 \u00d7 \\(\\frac{1}{3}\\)) = D'(80, 0)<br \/>\nHence the coordinates of the image are A'(0, 0), B'(0, 60), C'(80, 60), D'(80, 0)<\/p>\n<h3><a id=\"Dilations_Homework_&amp;_Practice_2.5\"><\/a>Dilations Homework &amp; Practice 2.5<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>The red \ufb01gure is congruent to the blue \ufb01gure. Describe a sequence of rigid motions between the \ufb01gures.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33370\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-93.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 93\" width=\"197\" height=\"189\" \/><\/p>\n<p>Answer:<br \/>\nSequence of rigid motion between the red and blue figure are<br \/>\n1. First rotate the blue figure 90 degrees in counterclockwise direction about the orgin because blue figure in 1st quadrant and red figure is in 3rd quadrant.<br \/>\n2. Then translate the image 1 unit left and 4 units down.<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33372\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-94.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 94\" width=\"195\" height=\"192\" \/><\/p>\n<p>Answer:<br \/>\nSequence of rigid motion between the red and blue figure are<br \/>\n1. First reflect the blue fiure about x-axis. The image after the reflection will lies in the 3rd quadrant with same orientation.<br \/>\n2. Then translate the image 5 units Right.<\/p>\n<p><strong>Tell whether the ratios form a proportion.<\/strong><\/p>\n<p>Question 3.<br \/>\n3 : 5 and 15 : 20<\/p>\n<p>Answer:<br \/>\nWhen two ratios are equal then it is called as proportion.<br \/>\nGiven,<br \/>\nGiven 3 : 5 and 15 : 20<br \/>\n3\/5 and 15\/20<br \/>\n3\/5 and 3\/4<br \/>\nSince the above two ratio are not equal hence they are not proportion<\/p>\n<p>Question 4.<br \/>\n2 to 3 and 12 to 18<\/p>\n<p>Answer:<br \/>\nWhen two ratios are equal then it is called as proportion.<br \/>\nGiven,<br \/>\n2 to 3 and 12 to 18<br \/>\n2\/3 and 12\/18<br \/>\n2\/3 and 2\/3<br \/>\nSince the above two ratio are equal hence they are proportion.<\/p>\n<p>Question 5.<br \/>\n7 : 28 and 12 : 48<\/p>\n<p>Answer:<br \/>\nWhen two ratios are equal then it is called as proportion.<br \/>\nGiven,<br \/>\n7 : 28 and 12 : 48<br \/>\n7\/28 and 12\/48<br \/>\n1\/4 and 1\/4<br \/>\nSince the above two ratio are equal hence they are proportion.<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><\/p>\n<p><strong>DESCRIBING RELATIONSHIPS<\/strong><br \/>\n<strong>Describe the relationship between the given point and the point A(8, 12) in terms of dilations.<\/strong> (See Exploration 1, p. 69.)<\/p>\n<p>Question 6.<br \/>\nB(16, 24)<\/p>\n<p>Answer:<br \/>\nGiven a point and its image: A(8,12), B(16, 24)<br \/>\nHere we can see that both x-coordinate and y-coordinate of image point have increased to double.<br \/>\nThis means that in this case, the image figure has become larger by the scale factor of 2 with respect to the origin.<br \/>\nHence the dilation scale factor is 2.<\/p>\n<p>Question 7.<br \/>\nC(2, 3)<\/p>\n<p>Answer:<br \/>\nGiven a point and its image: A(8,12), C(2, 3)<br \/>\nHere we can see that both x-coordinate and y-coordinate of image point has decreased to one-fourth.<br \/>\nThis means that in this case, the image figure has become smaller by the scale factor of 0.25 with respect to the origin.<br \/>\nThus the dilation scale factor is 1\/4.<\/p>\n<p>Question 8.<br \/>\nD(6, 9)<\/p>\n<p>Answer:<br \/>\nGiven a point and its image: A(8,12), D(6, 9)<br \/>\nHere we can see that both x-coordinate and y-coordinate of image point has decreased to three-fourth.<br \/>\nThis means that in this case the image figure has become smaller by the scale factor of 0.75 with respect to the origin.<br \/>\nThus the dilation scale factor is 3\/4.<\/p>\n<p><strong>IDENTIFYING A DILATION<\/strong><br \/>\n<strong>Tell whether the blue \ufb01gure is a dilation of the red \ufb01gure.<\/strong><\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33373\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-95.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 95\" width=\"178\" height=\"112\" \/><\/p>\n<p>Answer: Yes, the blue \ufb01gure is a dilation of the red \ufb01gure.<\/p>\n<p>Explanation:<br \/>\nWe observe that all the angles of the red figure are congruent to the angles of the red figure. Also there will be lines connecting the corresponding vertices meeting at a point. This means that blue figure is a dilation of the red figure.<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33374\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-96.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 96\" width=\"211\" height=\"110\" \/><\/p>\n<p>Answer: Yes, the blue \ufb01gure is a dilation of the red \ufb01gure.<\/p>\n<p>Explanation:<br \/>\nWe observe that all the angles of the red figure are congruent to the angles of the red figure. Also there will be lines connecting the corresponding vertices meeting at a point. This means that blue figure is a dilation of the red figure.<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33375\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-97.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 97\" width=\"203\" height=\"125\" \/><\/p>\n<p>Answer: No the blue \ufb01gure is not the dilation of the red \ufb01gure.<\/p>\n<p>Explanation:<br \/>\nThe Blue and red figure has same size and same shape but the blue figure is a reflection of vertical axis. So, the lines corresponding vertices of both figure does not meet at a point. This means that the blue figure is not the dilation of the red figure.<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33376\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-98.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 98\" width=\"189\" height=\"115\" \/><\/p>\n<p>Answer: Yes, the blue \ufb01gure is a dilation of the red \ufb01gure.<\/p>\n<p>Explanation:<br \/>\nWe observe that all the angles of red figure are congruent to the angles of red figure. Also their will be lines connecting the corresponding vertices meeting at a point. This means that blue figure is dilation of the red figure.<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33377\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-99.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 99\" width=\"163\" height=\"127\" \/><\/p>\n<p>Answer: Yes, the blue \ufb01gure is a dilation of the red \ufb01gure.<\/p>\n<p>Explanation:<br \/>\nWe observe that all the angles of red figure are congruent to the angles of red figure. Also their will be lines connecting the corresponding vertices meeting at a point. This means that blue figure is dilation of the red figure.<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33378\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-100.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 100\" width=\"130\" height=\"101\" \/><\/p>\n<p>Answer: No the blue \ufb01gure is not the dilation of the red \ufb01gure.<\/p>\n<p>Explanation:<br \/>\nBlue and red figure has same size and same shape but the blue figure is reflection about vertical axis. So, the lines corresponding vertices of both figure does not meet at a point. This means that the blue figure is not the dilation of the red figure.<\/p>\n<p><strong>DILATING A FIGURE<\/strong><br \/>\n<strong>The vertices of a \ufb01gure are given. Draw the \ufb01gure and its image after a dilation with the given scale factor. Identify the type of dilation.<\/strong><\/p>\n<p>Question 15.<br \/>\nA(1, 1), B(1, 4), C(3, 1); k = 4<\/p>\n<p>Answer:<br \/>\nWhen the points of given figure are dilated we simply multiply each x and y coordinate by the given scale factor.<br \/>\nP(x, y) = P'(x . a, y . a)<br \/>\nGiven points of the triangle: A(1, 1), B(1, 4), C(3, 1) and scale factor = 4<br \/>\nDilating the figure by scale factor by 4<br \/>\nA(1, 1) = A'(1 \u00d7 4, 1 \u00d7 4) = A'(4, 4)<br \/>\nB(1, 4) = B'(1 \u00d7 4, 4 \u00d7 4) = B'(4, 16)<br \/>\nC(3, 1) = C'(3 \u00d7 4, 1 \u00d7 4) = C'(12, 4)<br \/>\nHence the coordinate of the image are A'(4, 4), B'(4, 16), C'(12, 4)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-49592\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Solution-Key-Chapter-2-Transformations-img_27-281x300.png\" alt=\"Big Ideas Math 8th Grade Solution Key Chapter 2 Transformations img_27\" width=\"281\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Solution-Key-Chapter-2-Transformations-img_27-281x300.png 281w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Solution-Key-Chapter-2-Transformations-img_27.png 602w\" sizes=\"(max-width: 281px) 100vw, 281px\" \/><\/p>\n<p>Question 16.<br \/>\nD(0, 2), E(6, 2), F(6, 4); k = 0.5<\/p>\n<p>Answer:<br \/>\nWhen the points of given figure are dilated we simply multiply each x and y coordinate by the given scale factor.<br \/>\nP(x, y) = P'(x . a, y . a)<br \/>\nGiven points of the triangle: D(0, 2), E(6, 2), F(6, 4) and scale factor = 0.5<br \/>\nDilating the figure by scale factor by 0.5<br \/>\nD(0, 2) = D'(0 \u00d7 0.25, 2 \u00d7 0.25) = D'(0, 1)<br \/>\nE(6, 2) = E'(6 \u00d7 0.25, 2 \u00d7 0.25) = E'(3, 1)<br \/>\nF(6, 4) = F'(6 \u00d7 0.25, 4 \u00d7 0.25) = F'(3, 2)<br \/>\nHence the coordinate of the image are D'(0, 1), E'(3, 1), F'(3, 2)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-49595\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-grade-solution-key-for-chapter-2-transformations-img_28-300x207.png\" alt=\"BIM 8th grade solution key for chapter 2 transformations img_28\" width=\"300\" height=\"207\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-grade-solution-key-for-chapter-2-transformations-img_28-300x207.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-grade-solution-key-for-chapter-2-transformations-img_28.png 755w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 17.<br \/>\nG(-2, -2), H(-2, 6), J(2, 6); k = 0.25<\/p>\n<p>Answer:<br \/>\nWhen the points of given figure are dilated we simply multiply each x and y coordinate by the given scale factor.<br \/>\nP(x, y) = P'(x . a, y . a)<br \/>\nGiven points of the triangle: G(-2, -2), H(-2, 6), J(2, 6) and scale factor = 0.25<br \/>\nG(-2, -2) = G'(-2 \u00d7 0.25, -2 \u00d7 0.25) = G'(-0.5, -0.5)<br \/>\nH(-2, 6) = H'(-2 \u00d7 0.25,6 \u00d7 0.25) = H'(-0.5, 1.5)<br \/>\nJ(2, 6) = G'(2 \u00d7 0.25, 6 \u00d7 0.25) = J'(0.5, 1.5)<br \/>\nHence the coordinate of the image are G'(-0.5, -0.5), H'(-0.5, 1.5), J'(0.5, 1.5)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-49711\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-Answers-Grade-8-Chapter-2-Transformations-img_29-243x300.png\" alt=\"Big Ideas Math Book Answers Grade 8 Chapter 2 Transformations img_29\" width=\"243\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-Answers-Grade-8-Chapter-2-Transformations-img_29-243x300.png 243w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-Answers-Grade-8-Chapter-2-Transformations-img_29.png 492w\" sizes=\"(max-width: 243px) 100vw, 243px\" \/><\/p>\n<p>Question 18.<br \/>\nM(2, 3), N(5, 3), P(5, 1); k = 3<\/p>\n<p>Answer:<br \/>\nWhen the points of given figure are dilated we simply multiply each x and y coordinate by the given scale factor.<br \/>\nP(x, y) = P'(x . a, y . a)<br \/>\nGiven points of the triangle: M(2, 3), N(5, 3), P(5, 1) and scale factor = 3<br \/>\nM(2, 3) = M'(2 \u00d7 3, 3 \u00d7 3) = M'(6, 9)<br \/>\nN(5, 3) = N'(5 \u00d7 3, 3 \u00d7 3) = N'(15, 9)<br \/>\nP(5, 1) = P'(5 \u00d7 3, 1 \u00d7 3) = P'(15, 3)<br \/>\nHence the coordinate of the image are M'(6, 9), N'(15, 9), P'(15, 3)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-49716\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-Solution-Key-img_30-300x223.png\" alt=\"Big Ideas Math Grade 8 Chapter 2 Solution Key img_30\" width=\"300\" height=\"223\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-Solution-Key-img_30-300x223.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-Solution-Key-img_30-768x571.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-Solution-Key-img_30.png 811w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 19.<br \/>\nQ(-3, 0), R(-3, 6), T(4, 6), U(4, 0); k = \\(\\frac{1}{3}\\)<\/p>\n<p>Answer:<br \/>\nWhen the points of given figure are dilated we simply multiply each x and y coordinate by the given scale factor.<br \/>\nP(x, y) = P'(x . a, y . a)<br \/>\nGiven,<br \/>\nQ(-3, 0), R(-3, 6), T(4, 6), U(4, 0) and scale factor = \\(\\frac{1}{3}\\)<br \/>\nQ(-3, 0) = Q'(-3 \u00d7 \\(\\frac{1}{3}\\), 0 \u00d7 \\(\\frac{1}{3}\\)) = Q'(-1, 0)<br \/>\nR(-3, 6) = R'(-3 \u00d7 \\(\\frac{1}{3}\\), 6 \u00d7 \\(\\frac{1}{3}\\)) = R'(-1, 2)<br \/>\nT(4, 6) = T'(4 \u00d7 \\(\\frac{1}{3}\\), 6 \u00d7 \\(\\frac{1}{3}\\)) = T'(4\/3, 2)<br \/>\nU(4, 0) = U'(4 \u00d7 \\(\\frac{1}{3}\\), 0 \u00d7 \\(\\frac{1}{3}\\)) = U'(4\/3, 0)<br \/>\nHence the coordinate of the image are Q'(-1, 0), R'(-1, 2), T'(4\/3, 2), U'(4\/3, 0)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-49719\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-ch-2-transformations-answer-key-img_31-300x240.png\" alt=\"Big Ideas Math Grade 8 ch 2 transformations answer key img_31\" width=\"300\" height=\"240\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-ch-2-transformations-answer-key-img_31-300x240.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-ch-2-transformations-answer-key-img_31.png 620w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 20.<br \/>\nV(-2, -2), W(-2, 3), X(5, 3), Y(5, -2); k = 5<\/p>\n<p>Answer:<br \/>\nWhen the points of given figure are dilated we simply multiply each x and y coordinate by the given scale factor.<br \/>\nP(x, y) = P'(x . a, y . a)<br \/>\nGiven,<br \/>\nV(-2, -2), W(-2, 3), X(5, 3), Y(5, -2), scaling factor = 5<br \/>\nDilating the figure by scale factor of 5<br \/>\nV(-2, -2) = V'(-2 \u00d7 5, -2 \u00d7 5) = V'(-10, -10)<br \/>\nW(-2, 3) = W'(-2 \u00d7 5, 3 \u00d7 5) = W'(-10, 15)<br \/>\nX(5, 3) = X'(5 \u00d7 5, 3 \u00d7 5) = X'(25, 15)<br \/>\nY(5, -2) = Y'(5 \u00d7 5, -2 \u00d7 5) = Y'(25, -10)<br \/>\nHence the coordinate of the image are V'(-10, -10),W'(-10, 15), X'(25, 15), Y'(25, -10)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-50826\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-ch-2-answer-key-img_32-300x248.png\" alt=\"Big Ideas Math Grade 8 ch 2 answer key img_32\" width=\"300\" height=\"248\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-ch-2-answer-key-img_32-300x248.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-ch-2-answer-key-img_32.png 591w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 21.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend \ufb01nds the coordinates of the image of \u25b3ABC after a dilation with a scale factor of 2. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33379\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-101.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 101\" width=\"337\" height=\"129\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-101.png 337w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-101-300x115.png 300w\" sizes=\"(max-width: 337px) 100vw, 337px\" \/><\/p>\n<p>Answer:<br \/>\nWhen the points of given figure are dilated we simply multiply each x and y coordinate by the given scale factor.<br \/>\nP(x, y) = P'(x . a, y . a)<br \/>\nGiven,<br \/>\nThe points of triangle: A(2, 5), B(2, 0), C(4, 0)<br \/>\nscale factor = 2<br \/>\nDilating the figure by scale factor of 2<br \/>\nA(2, 5) = A'(2 \u00d7 2, 5 \u00d7 2) = A'(4, 10)<br \/>\nB(2, 0) = B'(2 \u00d7 2, 0 \u00d7 2) = B'(4, 0)<br \/>\nC(4, 0) = C'(4 \u00d7 2, 0 \u00d7 2) = C'(8, 0)<br \/>\nHence the coordinate of the image are A'(4, 10), B'(4, 0), C'(8, 0)<br \/>\nBy this, we can say that my friend is correct.<\/p>\n<p><strong>FINDING A SCALE FACTOR<\/strong><br \/>\n<strong>The blue \ufb01gure is a dilation of the red \ufb01gure. Identify the type of dilation and \ufb01nd the scale factor.<\/strong><\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33380\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-102.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 102\" width=\"199\" height=\"184\" \/><\/p>\n<p>Answer:<br \/>\nScale factor = side length of image\/side length of original figure<br \/>\nScale factor = A&#8217;B&#8217;\/AB = 6\/3 = 2<br \/>\nScale factor = 2<br \/>\nHence, type of dilation is enlargement with scale factor of 2.<\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33381\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-103.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 103\" width=\"194\" height=\"191\" \/><\/p>\n<p>Answer:<br \/>\nScale factor = side length of image\/side length of original figure<br \/>\nScale factor = X&#8217;Y&#8217;\/XY= 2\/8 = 1\/4<br \/>\nScale factor = 1\/4<br \/>\nHence, the type of dilation is reduction with the scale factor of 1\/4<\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33382\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-104.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 104\" width=\"195\" height=\"186\" \/><\/p>\n<p>Answer:<br \/>\nScale factor = side length of image\/side length of the original figure<br \/>\nScale factor = J&#8217;K&#8217;\/JK = 15\/10 = 3\/2<br \/>\nScale factor = 3\/2<br \/>\nHence, the type of dilation is reduction with the scale factor of 3\/2<\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33383\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-105.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 105\" width=\"195\" height=\"193\" \/><\/p>\n<p>Answer:<br \/>\nScale factor = side length of image\/side length of original figure<br \/>\nScale factor = Q&#8217;R&#8217;\/QR = 4\/8 = 1\/2<br \/>\nScale factor = 1\/2<br \/>\nHence, type of dilation is reduction with scale factor of 1\/2<\/p>\n<p><strong>USING MORE THAN ONE TRANSFORMATION<\/strong><br \/>\n<strong>The vertices of a \ufb01gure are given. Find the coordinates of the image after the transformations given.<\/strong><\/p>\n<p>Question 26.<br \/>\nA(-5, 3), B(-2, 3), C(-2, 1), D(-5, 1)<br \/>\nRe\ufb02ect in the y-axis. Then dilate using a scale factor of 2.<\/p>\n<p>Answer:<br \/>\nWe know that when a point is reflected about y-axis then is x-coordinate becomes opposite.<br \/>\nA(-5, 3), B(-2, 3), C(-2, 1), D(-5, 1)<br \/>\nA(x, y) = A'(-x, y)<br \/>\nA(-5, 3) = A'(5, 3)<br \/>\nB(-2, 3) = B'(2, 3)<br \/>\nC(-2, 1) = C'(2, 1)<br \/>\nD(-5, 1) = D'(5, 1)<br \/>\nCoordinate of the image are A'(5, 3), B'(2, 3), C'(2, 1), D'(5, 1)<br \/>\nA(-5, 3), B(-2, 3), C(-2, 1), D(-5, 1)<br \/>\nRe\ufb02ect in the y-axis. Then dilate using a scale factor of 2<br \/>\nA'(5, 3) = A&#8221;(5 \u00d7 2, 3 \u00d7 2) = A&#8221;(10, 6)<br \/>\nB'(2, 3) = B&#8221;(2 \u00d7 2, 3 \u00d7 2) = B&#8221;(4, 6)<br \/>\nC'(2, 1) = C&#8221;(2 \u00d7 2, 1 \u00d7 2) = C&#8221;(4, 2)<br \/>\nD'(5, 1) = D&#8221;(5 \u00d7 2, 1 \u00d7 2) = D&#8221;(10, 2)<br \/>\nCoordinate of the image are A&#8221;(10, 6), B&#8221;(4, 6), C&#8221;(4, 2), D&#8221;(10, 2)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-50828\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-grade-8-chapter-2-solution-key-img_33-300x165.png\" alt=\"Big ideas math grade 8 chapter 2 solution key img_33\" width=\"300\" height=\"165\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-grade-8-chapter-2-solution-key-img_33-300x165.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-grade-8-chapter-2-solution-key-img_33.png 683w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 27.<br \/>\nF(-9, -9), G(-3, -6), H(-3, -9).<br \/>\nDilate using a scale factor of \\(\\frac{2}{3}\\). Then translate 6 units up.<\/p>\n<p>Answer:<br \/>\nWhen the points of given figure are dilated we simply multiply each x and y coordinate by the given scale factor.<br \/>\nP(x, y) = P'(x . a, y . a)<br \/>\nGiven,<br \/>\nF(-9, -9), G(-3, -6), H(-3, -9) and scale factor of \\(\\frac{2}{3}\\)<br \/>\nDilating the figure by scale factor of \\(\\frac{2}{3}\\)<br \/>\nF(-9, -9) = F'(-9 \u00d7 2\/3, -9 \u00d7 2\/3) = F'(-6, -6)<br \/>\nG(-3, -6) = G'(-3 \u00d7 2\/3, -6 \u00d7 2\/3) = G'(-2, -4)<br \/>\nH(-3, -9) = H'(-3 \u00d7 2\/3, -9 \u00d7 2\/3) = H'(-2, -6)<br \/>\nCoordinate of the image are F'(-6, -6), G'(-2, -4), H'(-2, -6)<br \/>\nNow translating above image 6 units up<br \/>\nF'(-6, -6), G'(-2, -4), H'(-2, -6) and a = 0, b = 6<br \/>\nF&#8221;(-6 + a, -6 + b) = F&#8221;(-6 + 0, -6 + 6) = F&#8221;(-6, 0)<br \/>\nG&#8221;(-2 + a, -4 + b) = G&#8221;(-2 + 0, -4 + 6) = G&#8221;(-2, 2)<br \/>\nH&#8221;(-2 + a, -6 + b) = H&#8221;(-2 + 0, -6 + 6) = H&#8221;(-2, 0)<br \/>\nCoordinate of the image are F&#8221;(-6, 0), G&#8221;(-2, 2), H&#8221;(-2, 0)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-50834\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-2-img_34-300x300.png\" alt=\"BIM Grade 8 Answers Chapter 2 img_34\" width=\"300\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-2-img_34-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-2-img_34-150x150.png 150w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-2-img_34.png 521w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 28.<br \/>\nJ(1, 1), K(3, 4), L(5, 1)<br \/>\nRotate 90\u00b0 clockwise about the origin. Then dilate using a scale factor of 3.<\/p>\n<p>Answer:<br \/>\nThe rotation of an object 90 degrees clockwise is equal to the rotation of 270 degrees counterclockwise.<br \/>\nWhen a point is rotated 270 degrees counterclockwise about the origin then both x and y-coordinates gets interchanged and the x-coordinate becomes the opposite.<br \/>\nA(x, y) = A'(y, -x)<br \/>\nJ(1, 1), K(3, 4), L(5, 1)<br \/>\nRotate 90\u00b0 clockwise about the origin.<br \/>\nJ(1, 1) = J'(1, -1)<br \/>\nK(3, 4) = K'(4, -3)<br \/>\nL(5, 1) = L'(1, -5)<br \/>\nCoordinate of the image are J'(1, -1), K'(4, -3), L'(1, -5)<br \/>\nNow dilate using a scale factor of 3.<br \/>\nWhen the points of given figure are dilated we simply multiply each x and y coordinate by the given scale factor.<br \/>\nP(x, y) = P'(x . a, y . a)<br \/>\nJ'(1, -1) = J&#8221;(1 . 3, -1 . 3) = J&#8221;(3, -3)<br \/>\nK'(4, -3) = K&#8221;(4 . 3, -3 . 3) = K&#8221;(12, -9)<br \/>\nL'(1, -5) = L&#8221;(1 . 3, -5 . 3) = L&#8221;(3, -15)<br \/>\nCoordinate of the image are J&#8221;(3, -3), K&#8221;(12, -9), L&#8221;(3, -15)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-50835\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Answers-Ch-2-transformations-img_35-257x300.png\" alt=\"BIM 8th Grade Answers Ch 2 transformations img_35\" width=\"257\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Answers-Ch-2-transformations-img_35-257x300.png 257w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Answers-Ch-2-transformations-img_35.png 485w\" sizes=\"(max-width: 257px) 100vw, 257px\" \/><\/p>\n<p>Question 29.<br \/>\n<strong>LOGIC<\/strong><br \/>\nYou can use a \ufb02ashlight and a shadow puppet (your hands) to project shadows on the wall.<br \/>\na. Identify the type of dilation.p<\/p>\n<p>Answer: The type of dilation is an enlargement<\/p>\n<p>b. What does the \ufb02ashlight represent?<\/p>\n<p>Answer: Flashlight represents center of dilation because all the line connecting shadow and hand meet at the flashlight.<br \/>\nc. The length of the ears on the shadow puppet is 3 inches. The length of the ears on the shadow is 4 inches. What is the scale factor?<\/p>\n<p>Answer: Scale factor = length of ears on shadow\/length of ears on puppet<br \/>\nScale factor = 4\/3<br \/>\nd. Describe what happens as the shadow puppet moves closer to the \ufb02ashlight. How does this affect the scale factor?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33384\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-106.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 106\" width=\"399\" height=\"211\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-106.png 399w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-106-300x159.png 300w\" sizes=\"(max-width: 399px) 100vw, 399px\" \/><\/p>\n<p>Answer:<br \/>\nAs the flashlight will move closer the shadow will become larger. Also, the scale factor will increase.<\/p>\n<p>Question 30.<br \/>\n<strong>REASONING<\/strong><br \/>\nA triangle is dilated using a scale factor of 3. The image is then dilated using a scale factor of \\(\\frac{1}{2}\\). What scale factor can you use to dilate the original triangle to obtain the \ufb01nal image? Explain.<\/p>\n<p>Answer:<br \/>\nGiven the first scale factor of triangle S1 = 3<br \/>\nGiven second scale factor of triangle S2 = 1\/2<br \/>\nWe know that the final scale factor S = S1 \u00d7 S2<br \/>\nFinal Scale factor S = 3 \u00d7 1\/2 = 3\/2<br \/>\nHence, the scale factor of the final image will be the multiplication of the first and second dilation scale factor and the final scale factor will be 3\/2.<\/p>\n<p><strong>CRITICAL THINKING<\/strong><br \/>\n<strong>The coordinate notation shows how the coordinates of a \ufb01gure are related to the coordinates of its image after transformations. What are the transformations? Are the \ufb01gure and its image congruent? Explain.<\/strong><\/p>\n<p>Question 31.<br \/>\n(x, y) \u2192 (2x + 4, 2y &#8211; 3)<\/p>\n<p>Answer:<br \/>\nGiven, (x, y) \u2192 (2x + 4, 2y &#8211; 3)<br \/>\nWe can see that both x-coordinate and y-coordinate has been multiplied by 2 this means that the point has been dilated by the scale factor of 2.<br \/>\nAlso, 4 has been added to x-coordinate while 3 is added to y-coordinate which means that obtained after the dilation has been translated 4 unit Right and 3 units Down.<br \/>\nThe final image will not be congruent because after the dilation the size of the image either increases or decreases that depend on the type of dilation.<\/p>\n<p>Question 32.<br \/>\n(x, y) \u2192 (-x &#8211; 1, y &#8211; 2)<\/p>\n<p>Answer:<br \/>\nGiven, (x, y) \u2192 (-x &#8211; 1, y &#8211; 2)<br \/>\nWe can see that 1 has been subtracted from x-coordinate while 2 is subtracted from y-coordinate which means that will image has translated 1 unit left and 2 units down. And also x-coordinate is opposite which means the image has been reflected about the y-axis.<br \/>\nHence, transforms translation of 1 unit left and 2 units down followed by reflection about y-axis.<\/p>\n<p>Question 33.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33216\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-107.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 107\" width=\"140\" height=\"58\" \/><\/p>\n<p>Answer:<br \/>\nGiven, (x, y) \u2192 (1\/3x, -1\/3y)<br \/>\nWe can see that both x-coordinate and y-coordinate has been multiplied by 2 this means that the point has been dilated by the scale factor of 1\/3. Also, y-coordinate is opposite which means that image obtained after the dilation has been reflected about the x-axis.<br \/>\nThus transforms are dilation with the scale factor of 1\/3 followed by reflection about the x-axis.<\/p>\n<p><strong>STRUCTURE<\/strong><br \/>\n<strong>The blue \ufb01gure is a transformation of the red \ufb01gure. Use coordinate notation to describe the transformation. Explain your reasoning.<\/strong><\/p>\n<p>Question 34.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33385\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-108.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 108\" width=\"197\" height=\"186\" \/><\/p>\n<p>Answer:<br \/>\nCoordinates of original figure A(1, 1) B(1, 2), C(2, 1)<br \/>\nCoordinates of red figure A'(2, 3) B'(2, 6), C'(4, 3)<br \/>\nScale factor of x-coordinate = x-coordinate of image\/x-coordinate of image = 2\/1 = 2<br \/>\nScale factor of y-coordinate = y-coordinate of image\/y-coordinate of image = 3\/1 = 3<br \/>\nThus to transfer the red-figure into the blue figure x-coordinate of all the points has been multiplied by 2 and the y-coordinate of all the points has been multiplied by 3.<\/p>\n<p>Question 35.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33217\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-109.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 109\" width=\"201\" height=\"200\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-109.png 201w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-109-150x150.png 150w\" sizes=\"(max-width: 201px) 100vw, 201px\" \/><\/p>\n<p>Answer:<br \/>\nCoordinates of original figure A(4, 4) B(4, 8), C(8, 8), D(8, 4)<br \/>\nCoordinates of red figure A'(1, 2) B'(1, 4), C'(2, 4), D'(2. 2)<br \/>\nScale factor of x-coordinate = x-coordinate of image\/x-coordinate of image = 1\/4 = 0.25<br \/>\nScale factor of y-coordinate = y-coordinate of image\/y-coordinate of image = 2\/4 = 1\/2 = 0.5<br \/>\nThus to transfer the red figure into the blue figure x-coordinate of all the points has been multiplied by 0.25 and the y-coordinate of all the points has been multiplied by 0.50<\/p>\n<p>Question 36.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nYou dilate a \ufb01gure using a scale factor of 2, and then translate it 3 units right. Your friend translates the same \ufb01gure 3 units right and then dilates it using a scale factor of 2. Are the images congruent? Explain.<\/p>\n<p>Answer:<br \/>\nBlue the final image in both the case will be of the same shape and size.<br \/>\nYes, the image in both cases will be the same.<\/p>\n<p>Question 37.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe vertices of a trapezoid are A(-2, 3), B(2, 3), C(5, -2), and D(-2, -2). Dilate the trapezoid with respect to vertex A using a scale factor of 2. What are the coordinates of the image? Explain the method you used.<\/p>\n<p>Answer:<br \/>\nWhen the points of a given figure are dilated about a point we simply multiply the distance of each side by the given scale factor. The coordinate of one point remains the same about which dilation occurs.<br \/>\nThe vertices of a trapezoid are A(-2, 3), B(2, 3), C(5, -2), and D(-2, -2).<br \/>\nScale factor = 2<br \/>\nSo, here the coordinate of point A(-2, 3) will remains the same but all the other coordinates of points B&#8217;, C&#8217;, D&#8217; will change according to the distance between each side of the trapezoid.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-50839\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Key-Grade-8-Chapter-2-transformations-img_36-300x213.png\" alt=\"Big Ideas Math Key Grade 8 Chapter 2 transformations img_36\" width=\"300\" height=\"213\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Key-Grade-8-Chapter-2-transformations-img_36-300x213.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Key-Grade-8-Chapter-2-transformations-img_36.png 574w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nImage of the figure after dilating by a scale factor of 2<br \/>\nA(-2, 3) = A'(-2, 3)<br \/>\nB(2, 3) = B'(6, 3)<br \/>\nC(5, -2) = C'(12, -7)<br \/>\nD(-2, -2) = D'(-2, -7)<br \/>\nThus the coordinate of the image are A'(-2, 3), B'(6, 3), C'(12, -7), D'(-2, -7)<\/p>\n<p>Question 38.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA \ufb01gure is dilated using a scale factor of -1. How can you obtain the image without using a dilation? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nWhen a figure is dilated using a scale factor of -1 then both the x and y-coordinate of the image will become opposite.<br \/>\nExample:<br \/>\nA'(x . -1, y . -1) = A'(-x, -y)<br \/>\nBut there are two ways to get the same image:<br \/>\n1. By rotating the figure 180 degrees clockwise or anticlockwise<br \/>\nA(x, y) rotating 180 degrees about the origin = A'(-x, -y)<br \/>\n2. By rotating the figure about the x-axis and y axis<br \/>\nA(x, y) reflecting about the origin = A'(-x, -y)<\/p>\n<h3><a id=\"Lesson_2.6_Similar_Figures\"><\/a>Lesson 2.6 Similar Figures<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p><strong>Work with a partner. Use geometry software.<\/strong><br \/>\na. For each pair of \ufb01gures whose vertices are given below, draw the \ufb01gures in a coordinate plane. Use dilations and rigid motions to try to obtain one of the \ufb01gures from the other \ufb01gure.<\/p>\n<ul>\n<li>A(-3, 6), B(0, -3), C(3, 6) and G(-1, 2), H(0, 1), J(1, 2)<\/li>\n<li>D(0, 0), E(3, 0), F(3, 3) and L(0, 0), M(0, 6), N(-6, 6)<\/li>\n<li>P(1, 0), Q(4, 2), R(7, 0) and X(-1, 0), Y(-4, 6), Z(-7, 0)<\/li>\n<li>A(-3, 2), B(-1, 2), C(-1, -1), D(-3, -1) and F(6, 4), G(2, 4), H(2, -2), J(6, -2)<\/li>\n<li>P(-2, 2), Q(-1, -1), R(1, -1), S(2, 2) and W(2, 8), X(3, 3), Y(7, 3), Z(8, 8)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-33218\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-110.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 110\" width=\"293\" height=\"248\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33219\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-111.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 111\" width=\"160\" height=\"214\" \/><br \/>\nb. Is a scale drawing represented by any of the pairs of \ufb01gures in part(a)? Explain your reasoning.<br \/>\nc. Figure A is a scale drawing of Figure B. Do you think there must be a sequence of transformations that obtains Figure A from Figure B? Explain your reasoning.<\/p>\n<p><strong>2.6 Lesson<\/strong><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 1.<br \/>\nA triangle has vertices D(0, 4), E(5, 4), and F(5, 0). Is \u25b3DEF similar to \u25b3ABC and \u25b3JKL in Example 1? Explain.<\/p>\n<p>Answer:<br \/>\nGiven coordinate of the triangle ABC: A(0, 3), B(3, 3), C(3, 0)<br \/>\nGiven coordinate of the triangle DEF: D(0, 4), E(5, 4), F(5, 0)<br \/>\nGiven coordinate of the triangle JKL: J(0, 6), K(6, 6), L(6, 0)<br \/>\nHere we can see that there is no fixed relation between the coordinate between triangle ABC and DEF or triangle ABC and JKL. So no triangle is dilation with the triangle ABC.<br \/>\nHence, triangle ABC is not similar \u25b3DEF and \u25b3JKL.<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 2.<br \/>\nCan you re\ufb02ect the red \ufb01gure \ufb01rst, and then perform the dilation to obtain the blue \ufb01gure? Explain.<\/p>\n<p>Answer:<br \/>\nBecause the final image will not depend on the order of transformation. When we will first reflect red figure then the image will be of the same size and after the dilation of the image obtained after reflection we will get the same image so we can use any two method but the final image will be the same<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 3.<br \/>\n<strong>IDENTIFYING SIMILAR FIGURES<\/strong><br \/>\nIn the coordinate plane at the left, determine whether Rectangle ABCD is similar to Rectangle EFGH. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33220\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-112.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 112\" width=\"192\" height=\"191\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-112.png 192w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-112-150x150.png 150w\" sizes=\"(max-width: 192px) 100vw, 192px\" \/><\/p>\n<p>Answer: No rectangle ABCD is not similar to rectangle EFGH<\/p>\n<p>Explanation:<br \/>\nBecause the orientation of rectangle ABCD is not the same as the rectangle EFGH. Also, rectangle ABCD is not dilated with rectangle EFGH. So there is no similarity transformation between rectangle ABCD and rectangle EFGH.<\/p>\n<p>Question 4.<br \/>\n<strong>SIMILARITY TRANSFORMATION<\/strong><br \/>\nThe red triangle is similar to the blue triangle. Describe a similarity transformation between the \ufb01gures.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33221\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-113.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 113\" width=\"179\" height=\"171\" \/><\/p>\n<p>Answer:<br \/>\nCoordinate of left vertex of the red triangle: A(5, 5)<br \/>\nCoordinate of the same vertex after dilation: A'(10, 10)<br \/>\nNow coordinate left vertex of the blue triangle: A&#8221;(0, 2)<br \/>\nSo, the value of a = 0 &#8211; 10 = -10 and b = 2 &#8211; 10 = -8<br \/>\nIt is given that the red triangle is similar to the blue triangle so the steps of transformation:<br \/>\nFirst, dilate the figure by the scale factor of 2 and then translate the image 10 units left and 8 units down.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 5.<br \/>\nA medical supplier sells gauze in large and small rectangular sheets. A large sheet has a length of 9 inches and an area of 45 square inches. A small sheet has a length of 4 inches and a width of 3 inches. Are the sheets similar? Justify your answer.<\/p>\n<p>Answer:<br \/>\nCondition for the rectangular sheets to be similar is that all the corresponding sides of bigger and smaller rectangular sheets should be in proportional.<br \/>\nArea of larger rectangular sheets a = 45 sq in<br \/>\nlength of larger rectangular sheets l1 = 9 in<br \/>\nWidth = a\/l = 45\/9 = 5 in<br \/>\nlength of smaller rectangular sheets l2 = 4 in<br \/>\nwidth of smaller rectangular sheets b2 = 3 in<br \/>\ncondition for similarity l1\/l2 = b1\/b2<br \/>\n9\/4 \u2260 5\/3<br \/>\nThese sheets are not similar<\/p>\n<p>Question 6.<br \/>\nThe sail on a souvenir boat is similar in shape to the sail on a sailboat. The sail on the sailboat is in the shape of a right triangle with a base of 9 feet and a height of 24 feet. The height of the souvenir\u2019s sail is 3 inches. What is the base of the souvenir\u2019s sail?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33222\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-114.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 114\" width=\"184\" height=\"212\" \/><\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nThe base of sail on sailboat b1 = 9 ft<br \/>\nheight of sail on sailboat h1 = 24 ft<br \/>\nGiven height of sail on souvenir boat: h2 = 3in = 0.25 ft<br \/>\nh1\/h2 = b1\/b2<br \/>\n24\/0.25 = 9\/h2<br \/>\nh2 = (9 \u00d7 0.25)\/24 = 0.9375 ft = 1.125 in<br \/>\nThus the height of sail of a souvenir boat is 1.125 in<\/p>\n<p>Question 7.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA coordinate plane is used to represent a cheerleading formation. The vertices of the formation are A(4, 4), B(0, 8), C(4, 4), and D(0, 6). A choreographer creates a new formation similar to the original formation. Three vertices of the new formation are J(-2, -2), K(0, -4), and L(2, -2). What is the location of the fourth vertex? Explain.<\/p>\n<p>Answer:<br \/>\nThe vertices of the formation are A(4, 4), B(0, 8), C(4, 4), and D(0, 6). A choreographer creates a new formation similar to the original formation.<br \/>\nWe observe the image point carefully that both the x and y coordinate of the image point is just half of the original point and each y-coordinate is opposite.<br \/>\nA(4, 4) = J(-2, -2)<br \/>\nB(0, 8) = K(0, -4)<br \/>\nC(4, 4) = L(2, -2)<br \/>\nD(0, 6) = M(x, y)<br \/>\nThis means that the point A, B, C are dilated by using a scale factor of 0.5 and the image obtained from the dilation is reflected about the x-axis.<br \/>\nSo, the image point is D(0, 6) = M(0, -3)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-51215\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-img_37-248x300.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations img_37\" width=\"248\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-img_37-248x300.png 248w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2-Transformations-img_37.png 440w\" sizes=\"(max-width: 248px) 100vw, 248px\" \/><\/p>\n<h3><a id=\"Similar_Figures_Homework_&amp;_Practice_2.6\"><\/a>Similar Figures Homework &amp; Practice 2.6<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Tell whether the blue \ufb01gure is a dilation of the red \ufb01gure.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33223\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-115.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 115\" width=\"181\" height=\"97\" \/><\/p>\n<p>Answer: No<\/p>\n<p>Explanation:<br \/>\nBecause the shape and size of both red and blue figure are the same which is not the property of dilation. The blue figure is the result of the reflection of the red figure 180 degrees in the clockwise or counterclockwise direction.<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33224\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-116.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 116\" width=\"221\" height=\"72\" \/><\/p>\n<p>Answer: Yes<\/p>\n<p>Explanation:<br \/>\nWhen we see both red and blue figures closely we observe that all the angles of the red figure are congruent to the blue figure. Also, there will be the lines connecting corresponding vertices meeting at a point. This means that the blue figure is a dilation of red figure.<\/p>\n<p>Question 3.<br \/>\nYou solve the equation S = lw + 2wh for w. Which equation is correct?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33225\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-117.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 117\" width=\"453\" height=\"101\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-117.png 453w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-117-300x67.png 300w\" sizes=\"(max-width: 453px) 100vw, 453px\" \/><\/p>\n<p>Answer: Option C<\/p>\n<p>Explanation:<br \/>\nS = lw + 2wh<br \/>\nlw + 2wh = S<br \/>\nTaking w as a common factor<br \/>\nw(l + 2h) = s<br \/>\nw = s\/(l + 2h)<br \/>\nThus the correct answer is option C.<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><br \/>\n<strong>TRANSFORMING FIGURES<\/strong><br \/>\n<strong>The vertices of a pair of \ufb01gures are given. Determine whether a scale drawing is represented by the pair of \ufb01gures.<\/strong> (See Exploration 1, p. 77.)<\/p>\n<p>Question 4.<br \/>\nA(-8, -2), B(-4, 2), C(-4, -2) and G(2, -1), H(4, -1), J(2, -3)<\/p>\n<p>Answer: Yes<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-51218\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answer-Key-Chapter-2-Transformations-img_38-300x161.png\" alt=\"BIM Grade 8 Answer Key Chapter 2 Transformations img_38\" width=\"300\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answer-Key-Chapter-2-Transformations-img_38-300x161.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answer-Key-Chapter-2-Transformations-img_38-768x411.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answer-Key-Chapter-2-Transformations-img_38.png 838w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nAfter plotting both triangles we see that the original figure is exactly double of the image. Each side of the original triangle is double the length of the image triangle. So given vertices pair represent a scale drawing.<br \/>\nScale factor = 2<\/p>\n<p>Question 5.<br \/>\nA(0, 3), B(3, 4), C(5, 3), D(3, 2) and F(-4, 4), G(-1, 5), H(5, 3), J(3, 2)<\/p>\n<p>Answer: No<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-51219\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Ch-2-img_39-300x140.png\" alt=\"BIM Grade 8 Answers Ch 2 img_39\" width=\"300\" height=\"140\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Ch-2-img_39-300x140.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Ch-2-img_39-768x357.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Ch-2-img_39.png 890w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nAfter plotting both given figures we can see that there is no transformation relation between the original figure and the image figure. So, the given vertices pair does not represent a scale drawing.<\/p>\n<p><strong>IDENTIFYING SIMILAR FIGURES<\/strong><br \/>\n<strong>Determine whether the \ufb01gures are similar. Explain your reasoning<\/strong>.(See Exploration 1, p. 77.)<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33226\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-118.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 118\" width=\"194\" height=\"189\" \/><\/p>\n<p>Answer: Rectangle ABCD is similar to rectangle EFGH.<\/p>\n<p>Explanation:<br \/>\nBecause when you see both the given figure we can see that all the corresponding angles of rectangle ABCD and rectangle EFGH are equal. And also the corresponding sides of both rectangle are in proportional.<br \/>\n\u2220A = \u2220E, \u2220B = \u2220F, \u2220C = \u2220G, \u2220D = \u2220H<br \/>\nAB\/EF = BC\/FG = GH\/CD = DA\/HE = 1\/2<br \/>\nHence rectangle ABCD is similar to rectangle EFGH.<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33227\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-119.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 119\" width=\"196\" height=\"194\" \/><\/p>\n<p>Answer: Both the triangle are not similar<\/p>\n<p>Explanation:<br \/>\nBecause when you see both the given figure we can see that all the corresponding angles of triangle ABC and triangle JKL are equal. And also the corresponding sides of both triangles are not proportional.<br \/>\nAB\/JK \u2260 KL\/BC \u2260 CA\/LJ<br \/>\nHence triangle ABC is not similar to triangle JKL<\/p>\n<p><strong>IDENTIFYING SIMILAR FIGURES<\/strong><br \/>\n<strong>Draw the \ufb01gures with the given vertices in a coordinate plane. Which \ufb01gures are similar? Explain your reasoning.<\/strong><\/p>\n<p>Question 8.<br \/>\nRectangle A: (0, 0), (4, 0), (4, 2), (0, 2)<br \/>\nRectangle B: (0, 0), (6, 0), (6, 3), (0, 3)<br \/>\nRectangle C: (0, 0), (4, 0), (4, 2), (0, 2)<\/p>\n<p>Answer: Rectangle A and B are similar<\/p>\n<p>Explanation:<br \/>\nRectangle A: (0, 0), (4, 0), (4, 2), (0, 2)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-51442\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-Transformations-img_39i-300x202.png\" alt=\"Big Ideas Math Grade 8 Chapter 2 Transformations img_39(i)\" width=\"300\" height=\"202\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-Transformations-img_39i-300x202.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-Transformations-img_39i.png 460w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nRectangle B: (0, 0), (6, 0), (6, 3), (0, 3)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-51444\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-Transformations-img_39ii-300x202.png\" alt=\"Big Ideas Math Grade 8 Chapter 2 Transformations img_39(ii)\" width=\"300\" height=\"202\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-Transformations-img_39ii-300x202.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-Transformations-img_39ii.png 683w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nRectangle C: (0, 0), (4, 0), (4, 2), (0, 2)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-51445\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-Transformations-img_39iii-300x202.png\" alt=\"Big Ideas Math Grade 8 Chapter 2 Transformations img_39(iii)\" width=\"300\" height=\"202\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-Transformations-img_39iii-300x202.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-Transformations-img_39iii.png 460w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nBy seeing the above figure we can say that rectangle A and rectangle B are similar and rectangle A and Rectangle C are congruent.<\/p>\n<p>Question 9.<br \/>\nFigureA: (4, 2), (2, 2), (2, 0), (4, 0)<br \/>\nFigure B: (1, 4), (4, 4), (4, 1), (1, 1)<br \/>\nFigure C: (2, 1), (5, 1), (5, 3), (2, 3)<\/p>\n<p>Answer: Rectangle A and B are similar<\/p>\n<p>Explanation:<br \/>\nFigureA: (4, 2), (2, 2), (2, 0), (4, 0)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-51448\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-Transformations-img_40i-300x209.png\" alt=\"Big Ideas Math Grade 8 Chapter 2 Transformations img_40(i)\" width=\"300\" height=\"209\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-Transformations-img_40i-300x209.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-Transformations-img_40i.png 442w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nFigure B: (1, 4), (4, 4), (4, 1), (1, 1)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-51449\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-Transformations-img_40ii-300x268.png\" alt=\"Big Ideas Math Grade 8 Chapter 2 Transformations img_40(ii)\" width=\"300\" height=\"268\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-Transformations-img_40ii-300x268.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-Transformations-img_40ii.png 496w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nFigure C: (2, 1), (5, 1), (5, 3), (2, 3)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-51450\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-Transformations-img_40iii-300x209.png\" alt=\"Big Ideas Math Grade 8 Chapter 2 Transformations img_40(iii)\" width=\"300\" height=\"209\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-Transformations-img_40iii-300x209.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-2-Transformations-img_40iii.png 519w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nRectangles A and B are similar because in rectangle A and B all the corresponding angles are equal and also all the corresponding sides are equal.<\/p>\n<p><strong>DESCRIBING A SIMILARITY TRANSFORMATION<\/strong><br \/>\n<strong>The red \ufb01gure is similar to the blue \ufb01gure. Describe a similarity transformation between the \ufb01gures.<\/strong><\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33228\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-120.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 120\" width=\"237\" height=\"193\" \/><\/p>\n<p>Answer:<br \/>\n1. First rotate the red figure 90 degrees anticlockwise because the red figure is in the first quadrant and the blue figure is in the second quadrant.<br \/>\n2. Then dilate the image obtained after the rotation by the scale factor of 2 because the blue figure is double the size of the red figure.<br \/>\nScale factor = side of the image\/side of the original figure = 4\/2 = 2<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33229\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-121.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 121\" width=\"197\" height=\"188\" \/><\/p>\n<p>Answer:<br \/>\nFirst, dilate the red figure by the scale figure of 3 because the blue figure is triple the size of red figure.<br \/>\nscale factor = side of image\/side of original figure = 6\/2 = 3<\/p>\n<p>Question 12.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA barrier in the shape of a rectangle is used to retain oil spills. On a blueprint, a similar barrier is 9 inches long and 2 inches wide. The width of the actual barrier is 1.2 miles. What is the length of the actual barrier?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33230\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-122.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 122\" width=\"160\" height=\"102\" \/><\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nWidth of the actual barrier = 1.2 miles<br \/>\nWidth of the barrier in the blueprint = 2 inches<br \/>\n2 inch dimension of blueprint = 1.2 miles of original<br \/>\nSo, 1 inch dimension of blueprint = 1.2\/2 = 0.6 miles.<br \/>\nSince the length of the barrier in the blueprint = 9 inches,<br \/>\nThus the length of the actual barrier = 9(0.6) = 5.4 miles.<\/p>\n<p>Question 13.<br \/>\n<strong>LOGIC<\/strong><br \/>\nAre the following \ufb01gures always, sometimes, or never similar? Explain.<br \/>\na. two triangles<br \/>\nb. two squares<br \/>\nc. two rectangles<\/p>\n<p>Answer:<br \/>\na. Two triangles sometimes two triangles are similar when all the corresponding angles are equal and all the corresponding sides lengths are in proportion.<br \/>\nb. Two squares always two square are similar only when all the sides are proportional and all the angles are equal.<br \/>\nc. Two rectangles are similar when all the corresponding angles are equal but the lengths of the corresponding sides are not always in proportion.<\/p>\n<p>Question 14.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nCan you draw two quadrilaterals each having two 130\u00b0 angles and two 50\u00b0 angles that are not similar? Justify your answer.<\/p>\n<p>Answer:<br \/>\nQuadrilateral 1: 50\u00b0, 50\u00b0, 130\u00b0, 130\u00b0 (trapezoid)<br \/>\nQuadrilateral 2: 50\u00b0, 130\u00b0, 50\u00b0, 130\u00b0 (parallelogram)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-51588\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-ch-2-transformations-answer-key-img_41-300x256.png\" alt=\"Big Ideas Math Grade 8 ch 2 transformations answer key img_41\" width=\"300\" height=\"256\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-ch-2-transformations-answer-key-img_41-300x256.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-ch-2-transformations-answer-key-img_41.png 443w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 15.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe sign is rectangular.<br \/>\na. You increase each side length by 20%. Is the new sign similar to the original? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nYou increase each side length by 20%<br \/>\nScale factor = 1 + percentage increase\/100 = 1 + 20\/100 = 1.2<\/p>\n<p>b. You increase each side length by 6 inches. Is the new sign similar to the original? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33231\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-123.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 123\" width=\"179\" height=\"142\" \/><\/p>\n<p>Answer:<br \/>\nNo, because when length and width are of a different size then adding 6 inches on each side will not increase the figure in a fixed proportion. So the corresponding length will be not proportional. This means that both the figure will be not in dilation, hence not similar.<\/p>\n<p>Question 16.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA person standing 20 feet from a streetlight casts a shadow as shown. How many times taller is the streetlight than the person? Assume the triangles are similar.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33232\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-124.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 124\" width=\"248\" height=\"168\" \/><\/p>\n<p>Answer:<br \/>\nLength of shadow l1 = 10 ft<br \/>\nheight of man b1 = 6 ft<br \/>\nTotal length of bigger triangle l2 = 20 + 10 = 30 ft<br \/>\nl1\/l2 = b1\/b2<br \/>\n10\/30 = 6\/b2<br \/>\nb2 = 180\/10<br \/>\nb2 = 18 ft<br \/>\nThe ratio of the height of streetlight and man is: 18\/6 = 3<br \/>\nHence, the streetlight is 3 times taller than that person.<\/p>\n<p>Question 17.<br \/>\n<strong>GEOMETRY<\/strong><br \/>\nUse a ruler to draw two different isosceles triangles similar to the one shown. Measure the heights of each triangle.<br \/>\na. Are the ratios of the corresponding heights equivalent to the ratios of the corresponding side lengths?<\/p>\n<p>Answer:<br \/>\nb1\/b2 = h1\/h2<br \/>\n6\/3 = 4\/2 = 2<br \/>\nHence the ratio of corresponding heights is equivalent to the ratio of corresponding side lengths.<\/p>\n<p>b. Do you think this is true for all similar triangles? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33233\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-125.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 125\" width=\"197\" height=\"198\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-125.png 197w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-125-150x150.png 150w\" sizes=\"(max-width: 197px) 100vw, 197px\" \/><\/p>\n<p>Answer:<br \/>\nYes, this will be true for all the similar triangles because the heights of the two similar triangles are multiplied by the same amount as the sides.<\/p>\n<p>Question 18.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nGiven \u25b3ABC \u223c \u25b3DEF and \u25b3DEF \u223c \u25b3JKL, is \u25b3ABC \u223c \u25b3JKL? Justify your answer.<\/p>\n<p>Answer:<br \/>\nWhen \u25b3ABC is similar to \u25b3DEF and \u25b3DEF is similar to \u25b3JKL, then \u25b3ABC is similar to \u25b3JKL.<\/p>\n<h3><a id=\"Lesson_2.7_Perimeters_and_Areas_of_Similar_Figures\"><\/a>Lesson 2.7 Perimeters and Areas of Similar Figures<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p><strong>Work with a partner. Draw a rectangle in the coordinate plane.<\/strong><br \/>\na. Dilate your rectangle using each indicated scale factor k. Then complete the table for the perimeter P of each rectangle. Describe the pattern.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33234\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-126.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 126\" width=\"634\" height=\"187\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-126.png 634w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-126-300x88.png 300w\" sizes=\"(max-width: 634px) 100vw, 634px\" \/><br \/>\nb. Compare the ratios of the perimeters to the ratios of the corresponding side lengths. What do you notice?<br \/>\nc. Repeat part(a) to complete the table for the area A of each rectangle. Describe the pattern.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33235\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-127.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 127\" width=\"409\" height=\"109\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-127.png 409w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-127-300x80.png 300w\" sizes=\"(max-width: 409px) 100vw, 409px\" \/><br \/>\nd. Compare the ratios of the areas to the ratios of the corresponding side lengths. What do you notice?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33236\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-128.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 128\" width=\"160\" height=\"194\" \/><br \/>\ne. The rectangles shown are similar. You know the perimeter and the area of the red rectangle and a pair of corresponding side lengths. How can you \ufb01nd the perimeter of the blue rectangle? the area of the blue rectangle?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33424\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-500.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 500\" width=\"195\" height=\"138\" \/><\/p>\n<p><strong>2.7 Lesson<\/strong><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 1.<br \/>\nThe height of Figure A is 9 feet. The height of a similar Figure B is 15 feet. What is the value of the ratio of the perimeter of A to the perimeter of B?<\/p>\n<p>Answer: The ratio of the perimeter of A to B is 3\/5<\/p>\n<p>Explanation:<br \/>\nWe know that when two figures are similar then the value of the ratio of their perimeter is equal to the value of the ratio of their corresponding side lengths.<br \/>\nPerimeter of figure A\/Perimeter of figure B = Height of figure A\/Height of figure B<br \/>\nPerimeter of figure A\/Perimeter of figure B = 9\/15 = 3\/5<br \/>\nThus the ratio of the perimeter of A to B is 3\/5<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 2.<br \/>\nThe base of Triangle P is 8 meters. The base of a similar Triangle Q is 7 meters. What is the value of the ratio of the area of P to the area of Q?<\/p>\n<p>Answer:<br \/>\nWe know that when two figures are similar then the value of the ratio of their area is equal to the square of the value of the ratio of their corresponding side lengths.<br \/>\nThe base of Triangle P is 8 meters. The base of a similar Triangle Q is 7 meters.<br \/>\nb1 = 8 m<br \/>\nb2 = 7 m<br \/>\nArea of triangle P\/Area of triangle Q = base of triangle P\/base of triangle Q<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><strong>COMPARING PERIMETERS OF SIMILAR FIGURES<\/strong><br \/>\n<strong>Find the value of the ratio (red to blue) of the perimeters of the similar \ufb01gures.<\/strong><\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33237\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-130.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 130\" width=\"205\" height=\"76\" \/><\/p>\n<p>Answer:<br \/>\nWe know that when two figures is similar then the value of the ratio of their perimeter is equal to the value of the ratio of their corresponding side lengths.<br \/>\nPerimeter of figure A\/Perimeter of figure B = Side length of figure A\/Side length of figure B<br \/>\nl1 = 9<br \/>\nl2 = 7<br \/>\nPerimeter of red figure\/Perimeter of blue figure = Side length of red figure\/Side length of blue figure<br \/>\nPerimeter of red figure\/Perimeter of blue figure = 9\/7<br \/>\nThus the ratio of the perimeter of red to blue figure is 9\/7<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33238\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-131.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 131\" width=\"120\" height=\"111\" \/><\/p>\n<p>Answer:<br \/>\nWe know that when two figures is similar then the value of the ratio of their perimeter is equal to the value of the ratio of their corresponding side lengths.<br \/>\nPerimeter of figure A\/Perimeter of figure B = Side length of figure A\/Side length of figure B<br \/>\nb1 = 8<br \/>\nb2 = 10<br \/>\nPerimeter of red figure\/Perimeter of blue figure = base length of red figure\/base length of blue figure<br \/>\nPerimeter of red figure\/Perimeter of blue figure = 8\/10 = 4\/5<br \/>\nThus the ratio of the perimeter of red to blue triangle is 4\/5<\/p>\n<p><strong>COMPARING AREAS OF SIMILAR FIGURES<\/strong><br \/>\n<strong>Find the value of the ratio (red to blue) of the areas of the similar \ufb01gures.<\/strong><\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33239\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-132.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 132\" width=\"242\" height=\"81\" \/><\/p>\n<p>Answer:<br \/>\nWe know that when two figures is similar then the value of the ratio of their perimeter is equal to the value of the ratio of their corresponding side lengths.<br \/>\nPerimeter of figure A\/Perimeter of figure B = (Side length of figure A\/Side length of figure B)\u00b2<br \/>\nl1 = 12<br \/>\nl2 = 8<br \/>\nPerimeter of red figure\/Perimeter of blue figure = side length of red figure\/side length of blue figure<br \/>\nPerimeter of red figure\/Perimeter of blue figure = (12\/8)\u00b2 = (3\/2)\u00b2 = 9\/4<br \/>\nThus the ratio of the perimeter of red to blue figure is 9\/4<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33240\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-133.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 133\" width=\"182\" height=\"97\" \/><\/p>\n<p>Answer:<br \/>\nWe know that when two figures is similar then the value of the ratio of their perimeter is equal to the value of the ratio of their corresponding side lengths.<br \/>\nArea of figure A\/Area of figure B = (Side length of A\/Side length of B)\u00b2<br \/>\nl1 = 12<br \/>\nl2 = 8<br \/>\nArea of red figure\/Area of blue figure = side length of red figure\/side length of blue figure<br \/>\nArea of red figure\/Area of blue figure = (4\/5)\u00b2 = 16\/225<br \/>\nThus the ratio of the perimeter of red to blue triangle is 16\/225<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 7.<br \/>\nTwo similar triangular regions are prepared for development.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33241\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-134.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 134\" width=\"597\" height=\"248\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-134.png 597w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-134-300x125.png 300w\" sizes=\"(max-width: 597px) 100vw, 597px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33242\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-136.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 136\" width=\"193\" height=\"188\" \/><br \/>\na. It costs $6 per foot to install fencing. How much does it cost to surround the forest with a fence?<\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nIt costs $6 per foot to install fencing.<br \/>\nPerimeter of grassland\/perimeter of forest = Height of grassland\/Height of forest<br \/>\nh1 = 60 yards<br \/>\nThe perimeter of grassland = 240 yards<br \/>\nHeight of forest h2 = 45 yards<br \/>\nPerimeter of grassland\/perimeter of forest = 60\/45<br \/>\n240\/ perimeter of forest = 60\/45<br \/>\nthe perimeter of forest = 180 yards<br \/>\nConvert from yards to feet<br \/>\n180 yards = 540 feet<br \/>\nThus the cost of fencing forest = 6 \u00d7 540 = $3,240<\/p>\n<p>b. The cost to prepare 1 square yard of grassland is $15 and the cost to prepare 1 square yard of forest is $25. Which region costs more to prepare? Justify your answer.<\/p>\n<p>Answer:<br \/>\nPerimeter of grassland\/perimeter of forest = (Height of grassland\/Height of forest)\u00b2<br \/>\nHeight of grassland h1 = 60 yard<br \/>\nHeight of forest h2 = 45 yards<br \/>\nArea of grassland = 2400 yd\u00b2<br \/>\nCost to prepare 1 sq yd of grassland = $15<br \/>\nCost to prepare 1 sq yd of forest = $25<br \/>\nArea of forest = (2400 \u00d7 9)\/16<br \/>\nThus the area of forest is 1350 yd\u00b2<br \/>\nCost to prepare grassland = $15 \u00d7 2400 = $36,000<br \/>\nCost to prepare of forest = $25 \u00d7 1350 = $33,750<br \/>\nThus the grassland will cost more to prepare.<\/p>\n<p>Question 8.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou buy a new television with a screen similar in shape to your old television screen, but with an area four times greater. The size of a television screen is often described using the distance between opposite corners of the screen. Your old television has a 30-inch screen. What is the size of your new television screen? Explain.<\/p>\n<p>Answer:<br \/>\nArea of \u0394ABC\/Area of \u0394DEF = (Side length of AB\/Side length of DE)\u00b2<br \/>\nLet the area of the screen of old television be x<br \/>\nLet the area of the screen of new television be 4x<br \/>\nl1 = 30 in<br \/>\nArea of the screen of new television\/Area of the screen of new television= (distance of the screen of new television\/distance of the screen of old television)\u00b2<br \/>\n4x\/x = (distance of the screen of new television\/30)\u00b2<br \/>\ndistance of the screen of new television = 30 \u00d7 2 = 60 inch<br \/>\nHence the distance of the screen of the new television is 60 inches.<\/p>\n<h3><a id=\"Perimeters_and_Areas_of_Similar_Figures_Homework_&amp;_Practice_2.7\"><\/a>Perimeters and Areas of Similar Figures Homework &amp; Practice 2.7<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>The red \ufb01gure is similar to the blue \ufb01gure. Describe a similarity transformation between the \ufb01gures.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33425\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-2-Transformations-501.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 2 Transformations 501\" width=\"195\" height=\"190\" \/><\/p>\n<p>Answer:<br \/>\nFirst, dilate the red figure using the scale factor of 3 because the side lengths of the blue figure are 3 times the side length of the red figure.<br \/>\nScale factor = 6\/2 = 3<br \/>\nNow reflect the image obtained after a dilation about the y-axis because both red and blue triangle is facing each other.<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33243\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-137.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 137\" width=\"203\" height=\"190\" \/><\/p>\n<p>Answer:<br \/>\nFirst, dilate the red figure using the scale factor of 0.5 because the side lengths of the blue figure are 3 times the side length of the red figure.<br \/>\nScale factor = 2\/4 = 0.5<br \/>\nThen rotate the image obtained after dilation in direction 90 degrees clockwise about the origin.<\/p>\n<p><strong>Find the area of the \ufb01gure.<\/strong><\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33244\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-138.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 138\" width=\"129\" height=\"98\" \/><\/p>\n<p>Answer:<br \/>\nWe know that the formula for the area of trapezoid = Base \u00d7 height<br \/>\nh = 16 cm<br \/>\nb = 9 cm<br \/>\nArea of figure = 16 \u00d7 9 = 144 sq. cm<br \/>\nHence the area of the given figure is 144 sq. cm<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33245\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-139.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 139\" width=\"108\" height=\"124\" \/><\/p>\n<p>Answer:<br \/>\nh = 5 in<br \/>\nb = 3 in<br \/>\nWe know that,<br \/>\nA = 1\/2 \u00d7 b \u00d7 h<br \/>\nA = 1\/2 \u00d7 5 \u00d7 3<br \/>\nA = 7.5 sq. cm<br \/>\nThus the area of the given figure is 7.5 sq. cm<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33246\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-140.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 140\" width=\"166\" height=\"119\" \/><\/p>\n<p>Answer:<br \/>\nh = 5 km<br \/>\nb1 = 6 km<br \/>\nb2 = 8 km<br \/>\nWe know that,<br \/>\nArea of trapezoid = 1\/2 \u00d7 h \u00d7 (b1 + b2)<br \/>\nA = 1\/2 \u00d7 5 \u00d7 14 = 35 sq. km<br \/>\nHence the area of the trapezoid is 35 sq. km<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><br \/>\n<strong>COMPARING SIMILAR FIGURES<\/strong><br \/>\n<strong>Dilate the \ufb01gure using the indicated scale factor k. What is the value of the ratio (new to original) of the perimeters? the areas?<\/strong> (See Exploration 1, p. 83.)<\/p>\n<p>Question 6.<br \/>\na triangle with vertices (0, 0), (0, 2), and (2, 0); k = 3<\/p>\n<p>Answer:<br \/>\nWhen the points of a given figure are dilated we simply multiply each x-coordinate and y-coordinate by the given scale factor.<br \/>\nP(x, y) = P'(x . a, y . a)<br \/>\nwhere a is the scale factor<br \/>\nGiven a triangle with vertices (0, 0), (0, 2), and (2, 0); k = 3<br \/>\nA(0, 0) = A'(0 . 3, 0 . 3) = A'(0, 0)<br \/>\nB(0, 2) = B'(0 . 3, 2 . 3) = B'(0, 6)<br \/>\nC(2, 0) = C'(2 . 3, 0 . 3) = C'(6, 0)<br \/>\nThe coordinates of the image are A'(0, 0), B'(0, 6), C'(6, 0)<br \/>\nAB = \u221a(2 &#8211; 0)\u00b2 &#8211; (0 &#8211; 0)\u00b2 = 2<br \/>\nA&#8217;B&#8217; = \u221a(6 &#8211; 0)\u00b2 &#8211; (0 &#8211; 0)\u00b2 = 6<br \/>\nWe know that when two figure are similar then the value of the ratio of their perimeter is equal to the value of the ratio of their corresponding side lengths.<br \/>\nPerimeter of new triangle\/Perimeter of the original triangle = Distance of A&#8217;B&#8217;\/Distance of AB = 6\/2 = 3<br \/>\nArea of new triangle\/Area of the original triangle = (Distance of A&#8217;B&#8217;\/Distance of AB)\u00b2 = (6\/2)\u00b2 = 3\u00b2 = 9<\/p>\n<p>Question 7.<br \/>\na square with vertices (0, 0), (0, 4), (4, 4), and (4, 0); k = 0.5<\/p>\n<p>Answer:<br \/>\nWhen the points of a given figure are dilated we simply multiply each x-coordinate and y-coordinate by the given scale factor.<br \/>\nP(x, y) = P'(x . a, y . a)<br \/>\nwhere a is the scale factor<br \/>\na square with vertices (0, 0), (0, 4), (4, 4), and (4, 0); k = 0.5<br \/>\nA(0, 0) = A'(0 . 0.5, 0 . 0.5) = A'(0, 0)<br \/>\nB(0, 4) = B'(0 . 0.5, 4 . 0.5) = B'(0, 2)<br \/>\nC(4, 4) = C'(4 . 0.5, 4 . 0.5) = C'(2, 2)<br \/>\nD(4, 0) = D'(4 . 0.5, 0 . 0.5) = D'(2, 0)<br \/>\nCoordinates of the image are A'(0, 0), B'(0, 2), C'(2, 2), D'(2, 0)<br \/>\nAB = \u221a(4 &#8211; 0)\u00b2 + (0 &#8211; 0)\u00b2 = 4<br \/>\nA&#8217;B&#8217; = \u221a(2 &#8211; 0)\u00b2 + (0 &#8211; 0)\u00b2 = 2<br \/>\nWe know that when two figure are similar then the value of the ratio of their perimeter is equal to the value of the ratio of their corresponding side lengths.<br \/>\nPerimeter of new square\/Perimeter of the original square = Distance of A&#8217;B&#8217;\/Distance of AB = 2\/4 = 1\/2<br \/>\nArea of new square \/Area of the original square = (Distance of A&#8217;B&#8217;\/Distance of AB)\u00b2 = (2\/4)\u00b2 = 1\/4<\/p>\n<p><strong>PERIMETERS AND AREAS OF SIMILAR FIGURES<\/strong><br \/>\n<strong>Find the values of the ratios (red to blue) of the perimeters and areas of the similar \ufb01gures.<\/strong><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33247\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-141.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 141\" width=\"272\" height=\"86\" \/><\/p>\n<p>Answer:<br \/>\nWe know that when two figure are similar then the value of the ratio of their perimeter is equal to the value of the ratio of their corresponding side lengths.<br \/>\nPerimeter of red figure\/Perimeter of the blue figure = Distance of red figure\/Distance of blue figure= 11\/6<br \/>\nArea of red figure \/Area of the blue figure = (Distance of red figure\/Distance of blue figure)\u00b2 = (11\/6)\u00b2 = 121\/36<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33248\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-142.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 142\" width=\"223\" height=\"81\" \/><\/p>\n<p>Answer:<br \/>\nWe know that when two figure are similar then the value of the ratio of their perimeter is equal to the value of the ratio of their corresponding side lengths.<br \/>\nPerimeter of red figure\/Perimeter of the blue figure = Distance of red figure\/Distance of blue figure= 5\/8<br \/>\nArea of red figure \/Area of the blue figure = (Distance of red figure\/Distance of blue figure)\u00b2 = (5\/8)\u00b2 = 25\/64<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33249\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-143.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 143\" width=\"228\" height=\"112\" \/><\/p>\n<p>Answer:<br \/>\nWe know that when two figure are similar then the value of the ratio of their perimeter is equal to the value of the ratio of their corresponding side lengths.<br \/>\nPerimeter of red figure\/Perimeter of the blue figure = Distance of red figure\/Distance of blue figure= 4\/7<br \/>\nArea of red figure \/Area of the blue figure = (Distance of red figure\/Distance of blue figure)\u00b2 = (4\/7)\u00b2 = 16\/49<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33250\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-144.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 144\" width=\"312\" height=\"101\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-144.png 312w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-144-300x97.png 300w\" sizes=\"(max-width: 312px) 100vw, 312px\" \/><\/p>\n<p>Answer:<br \/>\nWe know that when two figure are similar then the value of the ratio of their perimeter is equal to the value of the ratio of their corresponding side lengths.<br \/>\nPerimeter of red figure\/Perimeter of the blue figure = Distance of red figure\/Distance of blue figure = 14\/9<br \/>\nArea of red figure \/Area of the blue figure = (Distance of red figure\/Distance of blue figure)\u00b2 = (14\/9)\u00b2 = 196\/81<\/p>\n<p><strong>USING SIMILAR FIGURES<\/strong><br \/>\n<strong>The \ufb01gures are similar. Find x.<\/strong><\/p>\n<p>Question 12.<br \/>\nThe ratio of the perimeters is 7 : 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33251\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-145.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 145\" width=\"274\" height=\"120\" \/><\/p>\n<p>Answer:<br \/>\nWe know that when two figure are similar then the value of the ratio of their perimeter is equal to the value of the ratio of their corresponding side lengths.<br \/>\nPerimeter of figure A\/Perimeter of the figure B = Distance of figure A\/Distance of figure B<br \/>\n7\/10 = x\/12<br \/>\nx = 84\/10<br \/>\nx = 8.4<br \/>\nThus the value of x is 8.4<\/p>\n<p>Question 13.<br \/>\nThe ratio of the perimeters is 8 : 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33252\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-146.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 146\" width=\"288\" height=\"114\" \/><\/p>\n<p>Answer:<br \/>\nWe know that when two figure are similar then the value of the ratio of their perimeter is equal to the value of the ratio of their corresponding side lengths.<br \/>\nPerimeter of figure A\/Perimeter of the figure B = Distance of figure A\/Distance of figure B<br \/>\n8\/5 = x\/16<br \/>\nx = 25.6<br \/>\nThus the value of x is 25.6<\/p>\n<p>Question 14.<br \/>\n<strong>COMPARING AREAS<\/strong><br \/>\nThe playing surfaces of two foosball tables are similar. The ratio of the corresponding side lengths is 10:7. What is the ratio of the areas?<\/p>\n<p>Answer:<br \/>\nArea of figure A \/Area of figure B = (Distance of figure A\/Distance of figure B)\u00b2<br \/>\nArea of figure A \/Area of figure B = (10\/7)\u00b2<br \/>\nArea of figure A \/Area of figure B = 100\/49<br \/>\nHence, the ratio of their areas is 100\/49<\/p>\n<p>Question 15.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nThe ratio of the side length of Square A to the side length of Square B is 4:9. The side length of Square A is 12 yards. What is the perimeter of Square B?<\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nThe ratio of the side length of Square A to the side length of Square B is 4\/9.<br \/>\nThe side length of Square A is 12 yards.<br \/>\nside length of Square A\/side length of Square B = 4\/9<br \/>\n12 \/side length of Square B = 4\/9<br \/>\nside length of Square B = 27 yards<br \/>\nWe know that,<br \/>\nThe perimeter of the square is = 4s<br \/>\nThe perimeter of the square B = 4 \u00d7 27 = 108 yards<\/p>\n<p>Question 16.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe cost of the piece of fabric shown is $1.31. What would you expect to pay for a similar piece of fabric that is 18 inches by 42 inches?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33253\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-147.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 147\" width=\"329\" height=\"186\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-147.png 329w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-147-300x170.png 300w\" sizes=\"(max-width: 329px) 100vw, 329px\" \/><\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nl = 21 in<br \/>\nw = 9 in<br \/>\nArea of the rectangle = l \u00d7 w<br \/>\nA = 21 \u00d7 9 = 189 sq. in<br \/>\nThe cost of the piece of fabric shown is $1.31<br \/>\nThe cost of 1 sq. in of fabric = 1.31\/189<br \/>\nl = 18 in<br \/>\nb = 42 in<br \/>\nArea of new fabric = 18 \u00d7 42 = 756 sq. in<br \/>\nGiven the cost of new fabric = 1.31\/189 \u00d7 756 = $5.24<br \/>\nHence the cost of the new fabric is $5.24<\/p>\n<p>Question 17.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA scale model of a merry-go-round and the actual merry-go-round are similar.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33254\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-148.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 148\" width=\"385\" height=\"223\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-148.png 385w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-148-300x174.png 300w\" sizes=\"(max-width: 385px) 100vw, 385px\" \/><br \/>\na. How many times greater is the base area of the actual merry-go-round than the base area of the scale model? Explain.<\/p>\n<p>Answer:<br \/>\nRadius of model merry go round = 6 in<br \/>\nRadius of actual merry go round = 10 ft = 120 in<br \/>\nArea of base of actual merry\/Area of base of model merry = (Radius of actual merry\/Radius of model merry)\u00b2<br \/>\nArea of base of actual merry\/Area of base of model merry = (120\/6)\u00b2 = 400<\/p>\n<p>b. What is the base area of the actual merry-go-round in square feet?<\/p>\n<p>Answer:<br \/>\nThe radius of model merry go round = 6 in<br \/>\nRadius of actual merry go round = 10 ft = 120 in<br \/>\nArea of base of actual merry = 450 sq. in<br \/>\nArea of base of actual merry\/Area of base of model merry = (Radius of actual merry\/Radius of model merry)\u00b2<br \/>\nArea of base of actual merry\/450 = (120\/6)\u00b2 = 400<br \/>\nArea of base of actual merry = 400 \u00d7 450 = 180000 sq. in = 1250 ft\u00b2<\/p>\n<p>Question 18.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nThe circumference of Circle K is \u03c0. The circumference of Circle L is 4\u03c0. What is the value of the ratio of their circumferences? of their radii? of their areas?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33255\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-149.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 149\" width=\"172\" height=\"137\" \/><\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nThe circumference of Circle K is \u03c0<br \/>\nThe circumference of Circle L is 4\u03c0.<br \/>\ncircumference of Circle = 2\u03c0r<br \/>\n2\u03c0r = \u03c0<br \/>\nThe radius of circle K r1 = 1\/2<br \/>\n2\u03c0r = 4\u03c0<br \/>\nThe radius of circle K r2 = 2<br \/>\nThe ratio of their circumference = \u03c0\/4\u03c0 = 1\/4<br \/>\nThe ratio of radius of both circle = 1\/4<br \/>\nThe ratio of their area = \u03c0(r1)\u00b2\/\u03c0(r2)\u00b2 = 1\/16<\/p>\n<p>Question 19.<br \/>\n<strong>GEOMETRY<\/strong><br \/>\nA triangle with an area of 10 square meters has a base of 4 meters. A similar triangle has an area of 90 square meters. What is the height of the larger triangle?<\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nA triangle with an area of 10 square meters has a base of 4 meters.<br \/>\nA similar triangle has an area of 90 square meters.<br \/>\nArea of the triangle = bh\/2<br \/>\nh = 2a\/b<br \/>\nh = (2 \u00d7 10)\/4<br \/>\nh = 5 meters<br \/>\nArea of larger triangle\/Area of smaller triangle = (height of larger triangle\/height of smaller triangle)\u00b2<br \/>\n90\/10 = (height of larger triangle\/5)\u00b2<br \/>\n3 = (height of larger triangle\/5)<br \/>\nThus the height of larger triangle = 3 \u00d7 5 = 15 meters<\/p>\n<p>Question 20.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou need two bottles of fertilizer to treat the \ufb02ower garden shown. How many bottles do you need to treat a similar garden with a perimeter of 105 feet?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33257\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-150.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 150\" width=\"286\" height=\"105\" \/><\/p>\n<p>Answer:<br \/>\nThe sides of the above figure are 4ft, 15 ft, 18 ft, 5 ft<br \/>\nPerimeter = 4ft + 15 ft + 18 ft + 5 ft = 42 ft<br \/>\nNumber of bottle of fertilizer used in the above garden = 2<br \/>\nNumber of bottle of fertilizer used in 1 ft = 2\/42<br \/>\nFertilizer used for 105 ft = 2\/42 \u00d7 105 = 5<br \/>\nThus 5 bottles will be used for 105 feet<\/p>\n<p>Question 21.<br \/>\n<strong>REPEATED REASONING<\/strong><br \/>\nThree square mirrors are used for a light re\ufb02ection experiment. The ratio of the side length of Mirror A to the side length of Mirror B is 5 : 6. The ratio of the area of Mirror B to the area of Mirror C is 16 : 25. The perimeter of Mirror C is 280 centimeters. What is the area of Mirror A? Justify your answer.<\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nThree square mirrors are used for a light re\ufb02ection experiment.<br \/>\nThe ratio of the side length of Mirror A to the side length of Mirror B is 5 : 6 = 5\/6<br \/>\nThe ratio of the area of Mirror B to the area of Mirror C is 16 : 25 = 16\/25<br \/>\nThe perimeter of Mirror C is 280 centimeters<br \/>\nSide length of mirror C = Perimeter\/4 = 280\/4 = 70 cm<br \/>\n(Side length of mirror B\/Side length of mirror C)\u00b2 = Area of mirror A\/Area of mirror B<br \/>\n(Side length of mirror B\/Side length of mirror C)\u00b2 = 16\/25<br \/>\n(Side length of mirror B\/Side length of mirror C) = 4\/5<br \/>\nThe side length of mirror B = 4\/5 \u00d7 Side length of mirror C<br \/>\nSide length of mirror B = 4\/5 \u00d7 70 = 56 cm<br \/>\nA = s \u00d7 s<br \/>\nA = 56 cm \u00d7 56 cm = 3136 sq. cm<br \/>\nArea of mirror A\/Area of mirror B = (Side length of mirror A\/Side length of mirror B)\u00b2<br \/>\nArea of mirror A\/3136 = (5\/6)\u00b2<br \/>\nArea of mirror A = 25\/36 \u00d7 3136<br \/>\nArea of mirror A = 2177.7 sq. cm<\/p>\n<h3><a id=\"Transformations_Connecting_Concepts\"><\/a>Transformations Connecting Concepts<\/h3>\n<p><strong>2 Connecting Concepts<\/strong><\/p>\n<p><strong>Using the Problem-Solving Plan<\/strong><\/p>\n<p>Question 1.<br \/>\nA scale drawing of a helipad uses a scale of 1 ft : 20 ft. The scale drawing has an area of 6.25 square feet. What is the area of the actual helipad?<br \/>\n<strong>Understand the problem.<\/strong><br \/>\nYou know the scale of the drawing and the area of the helipad in the drawing. You are asked to \ufb01nd the area of the actual helipad.<br \/>\n<strong>Make a plan.<\/strong><br \/>\nA scale drawing is similar to the actual object. So, use the scale 1 ft : 20 ft and the ratio 6.25 ft<sup>2<\/sup> : A ft<sup>2<\/sup> to write and solve a proportion that represents the area A of the actual helipad.<br \/>\n<strong>Solve and Check.<\/strong><br \/>\nUse the plan to solve the problem. Then check your solution.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33256\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-150.1.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 150.1\" width=\"266\" height=\"128\" \/><\/p>\n<p>Answer: 125 sq. ft<\/p>\n<p>Question 2.<br \/>\nThe locations of three cargo ships are shown in the coordinate plane. Each ship travels at the same speed in the same direction. After 1 hour, the x- and y-coordinates of Ship A increase 80%. Use a translation to describe the change in the locations of the ships. Then \ufb01nd the new coordinates of each ship.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33258\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-151.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 151\" width=\"241\" height=\"184\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33259\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-152.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 152\" width=\"172\" height=\"159\" \/><\/p>\n<p>Question 3.<br \/>\nAll circles are similar. A circle with a radius of 2 inches is dilated, resulting in a circle with a circumference of 22\u03c0 inches. What is the scale factor? Justify your answer.<\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nA circle with a radius of 2 inches is dilated, resulting in a circle with a circumference of 22\u03c0 inches.<br \/>\nC = 2\u03c0 . r<br \/>\n22\u03c0 = 2\u03c0 . 2<br \/>\np = 2\u03c0 . 2<br \/>\nThus the scale factor is 2.<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p><strong>Master Puppeteer<\/strong><\/p>\n<p>At the beginning of this chapter, you watched a STEAM Video called \u201cShadow Puppets.&#8221; You are now ready to complete the performance task related to this video, available at BigIdeasMath.com. Be sure to use the problem-solving plan as you work through the performance task.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33260\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-153.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 153\" width=\"281\" height=\"204\" \/><\/p>\n<h3>Transformations Connecting Concepts<\/h3>\n<p><strong>2 Chapter Review<\/strong><\/p>\n<p><strong>Review Vocabulary<\/strong><\/p>\n<p>Write the de\ufb01nition and give an example of each vocabulary term.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33261\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-154.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 154\" width=\"638\" height=\"115\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-154.png 638w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-154-300x54.png 300w\" sizes=\"(max-width: 638px) 100vw, 638px\" \/><\/p>\n<p><strong>Graphic Organizers<\/strong><br \/>\nYou can use a Summary Triangle to explain a concept. Here is an example of Summary Triangle for translating a figure.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33262\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-155.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 155\" width=\"466\" height=\"363\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-155.png 466w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-155-300x234.png 300w\" sizes=\"(max-width: 466px) 100vw, 466px\" \/><\/p>\n<p><strong>Choose and complete a graphic organizer to help you study the concept.<\/strong><\/p>\n<ol>\n<li>re\ufb02ecting a \ufb01gure<\/li>\n<li>rotating a \ufb01gure<\/li>\n<li>congruent \ufb01gures<\/li>\n<li>dilating a \ufb01gure<\/li>\n<li>similar \ufb01gures<\/li>\n<li>perimeters of similar \ufb01gures<\/li>\n<li>areas of similar \ufb01gures<\/li>\n<\/ol>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-33263\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-156.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 156\" width=\"325\" height=\"311\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-156.png 325w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-156-300x287.png 300w\" sizes=\"(max-width: 325px) 100vw, 325px\" \/><\/p>\n<p><strong>Chapter Self-Assessment<\/strong><\/p>\n<p>As you complete the exercises, use the scale below to rate your understanding of the success criteria in your journal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33170\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-157.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 157\" width=\"648\" height=\"93\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-157.png 648w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-157-300x43.png 300w\" sizes=\"(max-width: 648px) 100vw, 648px\" \/><\/p>\n<p><strong>2.1 Translations<\/strong> (pp. 43\u201348)<\/p>\n<p><strong>Tell whether the blue \ufb01gure is a translation of the red \ufb01gure.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33171\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-158.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 158\" width=\"205\" height=\"79\" \/><\/p>\n<p>Answer: No<\/p>\n<p>Explanation:<br \/>\nThe answer is no because in the case of translation the size of the figure does not change, only the position of the figure changes. But here the size of the blue figure is larger as compared to the red figure so this is not the translation. Here the blue figure is the result of the dilation of red figure.<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33172\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-159.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 159\" width=\"170\" height=\"84\" \/><\/p>\n<p>Answer: Yes<\/p>\n<p>Explanation:<br \/>\nYes, because in the case of translation the size of the figure does not change, only the position of the figure changes. Here the size of both blue figure and the red figure is the same but there is only a change in the position of the red figure to get blue figure. Here the blue figure is the result of the translation of the red figure.<\/p>\n<p>Question 3.<br \/>\nThe vertices of a quadrilateral are W(1, 2), X(1, 4), Y(4, 4), and Z(4, 2). Draw the \ufb01gure and its image after a translation 3 units left and 2 units down.<\/p>\n<p>Answer:<br \/>\nWe know that to translate a figure &#8216;a&#8217; units horizontally and &#8216;b&#8217; units vertically in the coordinate plane, &#8216;a&#8217; is added to x-coordinate and &#8216;b&#8217; is added to y-coordinate of the vertices.<br \/>\nA(x,y) = A'(x+a, y+b)<br \/>\nThe value a and b will be positive if shift is Right and Vertical Up and the value of a and b will be negative if shift is left and vertical Down.<br \/>\nGiven: W(1, 2), X(1, 4), Y(4, 4), and Z(4, 2) and a = -3, b = -2<br \/>\nW'(1+a, 2+b) = W'(1-3, 2-2) = W'(-2,0)<br \/>\nX'(1+a, 4+b) = X'(1-3, 4-2) = X'(-2,2)<br \/>\nY'(4+a, 4+b) = Y'(4-3, 4-2) = Y'(1, 2)<br \/>\nZ'(4+a, 2+b) = C'(4-3, 2-2) = Z'(1,0)<br \/>\nHence the coordinate of image are W'(-2,0), X'(-2,2), Y'(1, 2), Z'(1,0)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-51722\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-2-img_41-300x189.png\" alt=\"big ideas math answers grade 8 chapter 2 img_41\" width=\"300\" height=\"189\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-2-img_41-300x189.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-2-img_41.png 617w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 4.<br \/>\nThe vertices of a triangle are A(-1, -2), B(-2, 2), and C(-3, 0). Draw the \ufb01gure and its image after a translation 5 units right and 1 unit up.<\/p>\n<p>Answer:<br \/>\nWe know that to translate a figure &#8216;a&#8217; units horizontally and &#8216;b&#8217; units vertically in the coordinate plane, &#8216;a&#8217; is added to x-coordinate and &#8216;b&#8217; is added to y-coordinate of the vertices.<br \/>\nA(x,y) = A'(x+a, y+b)<br \/>\nThe value a and b will be positive if shift is Right and Vertical Up and the value of a and b will be negative if shift is left and vertical Down.<br \/>\nGiven: A(-1, -2), B(-2, 2), and C(-3, 0) and a = 5, b = 1<br \/>\nA'(-1+a, -2+b) = A'(-1-5, -2+1) = A'(4,-1)<br \/>\nB'(-2+a, 2+b) = B'(-2+5, 2+1) = B'(3,3)<br \/>\nC'(-3+a, 0+b) = C'(-3+5, 0+1) = C'(2, 1)<br \/>\nHence the coordinate of image are\u00a0A'(4,-1), B'(3,3), C'(2, 1)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-51723\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Chapter-2-Answer-Key-img_42-300x210.png\" alt=\"BIM Grade 8 Chapter 2 Answer Key img_42\" width=\"300\" height=\"210\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Chapter-2-Answer-Key-img_42-300x210.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Chapter-2-Answer-Key-img_42.png 646w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 5.<br \/>\nYour locker number is 20 and your friend\u2019s locker number is 33. Describe the location of your friend\u2019s locker relative to the location of your locker.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33266\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-159.1.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 159.1\" width=\"196\" height=\"228\" \/><\/p>\n<p>Answer:<br \/>\nThe location of my friend&#8217;s locker is first 1 locker Down and then 3 locker Right.<\/p>\n<p>Question 6.<br \/>\nTranslate the triangle 4 units left and 1 unit down. What are the coordinates of the image?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33173\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-160.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 160\" width=\"201\" height=\"194\" \/><\/p>\n<p>Answer:<br \/>\nWe know that to translate a figure &#8216;a&#8217; units horizontally and &#8216;b&#8217; units vertically in the coordinate plane, &#8216;a&#8217; is added to x-coordinate and &#8216;b&#8217; is added to y-coordinate of the vertices.<br \/>\nA(x,y) = A'(x+a, y+b)<br \/>\nThe value a and b will be positive if shift is Right and Vertical Up and the value of a and b will be negative if shift is left and vertical Down.<br \/>\nGiven: A(3, 5), B(6, 3), and C(4, 1) and a = -4, b = -1<br \/>\nA'(3+a, 5+b) = A'(3-4, 5-1) = A'(-1,4)<br \/>\nB'(6+a, 3+b) = B'(6-4, 3-1) = B'(2,2)<br \/>\nC'(4+a, 1+b) = C'(4-4, 1-1) = C'(0, 0)<br \/>\nHence the coordinate of image are A'(-1,4), B'(2,2), C'(0, 0)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-51724\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Answer-Key-Chapter-2-img_42-300x208.png\" alt=\"BIM 8th Grade Answer Key Chapter 2 img_42\" width=\"300\" height=\"208\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Answer-Key-Chapter-2-img_42-300x208.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Answer-Key-Chapter-2-img_42.png 521w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 7.<br \/>\nDescribe a translation of the airplane from point A to point B.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33174\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-161.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 161\" width=\"278\" height=\"159\" \/><\/p>\n<p>Answer:<br \/>\nFirst, move the aeroplane 6 units right from point A and then 4 units down.<\/p>\n<p><strong>2.2 Reflections<\/strong> (pp. 49 &#8211; 54)<\/p>\n<p><strong>Tell whether the blue \ufb01gure is a re\ufb02ection of the red \ufb01gure.<\/strong><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33175\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-162.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 162\" width=\"163\" height=\"90\" \/><\/p>\n<p>Answer:<br \/>\nNo, because in the above figure the plane of reflection is inclined at 45 degrees with the horizontal line. So, the reflected figure will be perpendicular to the original figure. But in the given figure both are facing each other. This means that the blue figure is not the reflection of red figure.<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33177\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-163.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 163\" width=\"163\" height=\"101\" \/><\/p>\n<p>Answer:<br \/>\nThe answer is no because the blue figure is not the mirror image of the red figure. The side of the red figure is not facing the side of the blue figure this means that the blue figure is not the reflection of red figure.<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33176\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-163.1.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 163.1\" width=\"129\" height=\"108\" \/><\/p>\n<p>Answer:<br \/>\nThe answer is yes because the blue figure is the mirror image of the red figure. The side of the red figure is facing the side of the blue figure this means that the blue figure is the reflection of red figure.<\/p>\n<p><strong>Draw the \ufb01gure and its re\ufb02ection in (a) the x-axis and (b) the y-axis. Identify the coordinates of the image.<\/strong><\/p>\n<p>Question 11.<br \/>\nA(2, 0), B(1, 5), C(4, 3)<\/p>\n<p>Answer:<br \/>\nA(x, y) = A'(x, -y)<br \/>\nGiven: A(2, 0), B(1, 5), C(4, 3)<br \/>\nReflection about x-axis:<br \/>\nA(2, 0) = A'(2, 0)<br \/>\nB(1, 5) = B'(1, -5)<br \/>\nC(4, 3) = C'(4, -3)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-51725\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-2-img_43-201x300.png\" alt=\"BIM Grade 8 Answers Chapter 2 img_43\" width=\"201\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-2-img_43-201x300.png 201w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-2-img_43.png 416w\" sizes=\"(max-width: 201px) 100vw, 201px\" \/><br \/>\nReflection about y-axis:<br \/>\nA(x, y) = A'(-x, y)<br \/>\nA(2, 0) = A'(-2, 0)<br \/>\nB(1, 5) = B'(-1, 5)<br \/>\nC(4, 3) = C'(-4, 3)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-51726\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-2-img_44-300x211.png\" alt=\"BIM Grade 8 Answers Chapter 2 img_44\" width=\"300\" height=\"211\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-2-img_44-300x211.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-2-img_44.png 578w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 12.<br \/>\nD(-5, -5), E(-5, 0), F(-2, -2), G(-2, -5)<\/p>\n<p>Answer:<br \/>\nGiven, D(-5, -5), E(-5, 0), F(-2, -2), G(-2, -5)<br \/>\nReflection about x-axis:<br \/>\nA(x, y) = A'(x, -y)<br \/>\nD(-5, -5) = D'(-5, 5)<br \/>\nE(-5, 0) = E'(-5, 0)<br \/>\nF(-2, -2) = F'(-2, 2)<br \/>\nG(-2, -5) = G'(-2, 5)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-51727\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-2-img_45-211x300.png\" alt=\"BIM Grade 8 Answers Chapter 2 img_45\" width=\"211\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-2-img_45-211x300.png 211w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-2-img_45.png 403w\" sizes=\"(max-width: 211px) 100vw, 211px\" \/><br \/>\nReflection about y-axis:<br \/>\nA(x, y) = A'(-x, y)<br \/>\nD(-5, -5) = D(5, -5)<br \/>\nE(-5, 0) = E'(5, 0)<br \/>\nF(-2, -2) = F'(2, -2)<br \/>\nG(-2, -5) = G'(2, -5)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-51728\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-2-img_46-300x163.png\" alt=\"BIM Grade 8 Answers Chapter 2 img_46\" width=\"300\" height=\"163\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-2-img_46-300x163.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-2-img_46-768x418.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-2-img_46.png 887w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 13.<br \/>\nThe vertices of a rectangle are E(-1, 1), F(-1, 3), G(-5, 3), and H(-5, 1). Find the coordinates of the \ufb01gure after re\ufb02ecting in the x-axis, and then translating 3 units right.<\/p>\n<p>Answer:<br \/>\nWe know that when a point is reflected about x-axis then y-coordinate becomes the opposite.<br \/>\nA(x, y) = A'(x, -y)<br \/>\nThe vertices of a rectangle are E(-1, 1), F(-1, 3), G(-5, 3), and H(-5, 1).<br \/>\nReflection about x-axis:<br \/>\nE(-1, 1) = E'(-1, -1)<br \/>\nF(-1, 3) = F'(-1, -3)<br \/>\nG(-5, 3) = G'(-5, 3)<br \/>\nH(-5, 1) = H'(-5, 1)<br \/>\nThus the coordinates of the image are E'(-1, -1), F'(-1, -3), G'(-5, 3), H'(-5, 1)<br \/>\nNow translating the image 3 units Right.<br \/>\nWe know that to translate a figure &#8216;a&#8217; units horizontally and &#8216;b&#8217; units vertically in coordinate plane, &#8216;a&#8217; is added to x-coordinate and &#8216;b&#8217; is added to y-coordinate of the vertices.<br \/>\nA(x,y) = A'(x+a, y+b)<br \/>\nThe value a and b will be positive if shift is Right and Vertical Up and the value of a and b will be negative if shift is left and vertical Down.<br \/>\nGiven: E'(-1, -1), F'(-1, -3), G'(-5, 3), H'(-5, 1) a = 3, b = 0<br \/>\nE&#8221;(-1 + a, -1 + b) = E&#8221;(-1 + 3, -1 + 0) = E&#8221;(2, -1)<br \/>\nF&#8221;(-1 + a, -3 + b) = F&#8221;(-1 + 3, -3 + 0) = F&#8221;(2, -3)<br \/>\nG&#8221;(-5 + a, 3 + b) = G&#8221;(-5 + 3, 3 + 0) = G&#8221;(-2, 3)<br \/>\nH&#8221;(-5 + a, 1 + b) = H&#8221;(-5 + 3, 1 + 0) = H&#8221;(-2, 1)<br \/>\nThus the coordinates of the image are E&#8221;(2, -1), F&#8221;(2, -3), G&#8221;(-2, 3), H&#8221;(-2, 1)<\/p>\n<p><strong>The coordinates of a point and its image after a re\ufb02ection are given. Identify the line of re\ufb02ection.<\/strong><\/p>\n<p>Question 14.<br \/>\n(-1, -3) \u2192 (1, -3)<\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\n(-1, -3) \u2192 (1, -3)<br \/>\nWe can see that the y-coordinate of both points and its image are the same but the x-coordinate of the image is the opposite of its points.<br \/>\nHence, Y-axis is the line of reflection.<\/p>\n<p>Question 15.<br \/>\n(2, 1) \u2192 (2, -1)<\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\n(2, 1) \u2192 (2, -1)<br \/>\nWe can see that the x-coordinate of both points and its image are the same but the y-coordinate of the image is the opposite of its points.<br \/>\nHence, X-axis is the line of reflection.<\/p>\n<p>Question 16.<br \/>\nYou perform an experiment involving angles of refraction with a laser pen. You point a laser pen from point L at a mirror along the red path and the image is a re\ufb02ection in the y-axis.<br \/>\na. Does the light reach a cat at point C? Explain.<\/p>\n<p>Answer:<br \/>\nYes, the light will reach at point C.<br \/>\nBecause the coordinate of point L is (4, 3) and the coordinate of point C is (-4, 3) and it is given problems that laser is reflected about the y-axis.<br \/>\nSo when point L(4, 3) is reflected about the y-axis its x-coordinates become opposite and y-coordinates remain the same.<br \/>\nSo when point L(4, 3) is reflected about the y-axis its image will be point C(-4, -3)<\/p>\n<p>b. You bounce the light off the mirror so its path is a re\ufb02ection. What line of re\ufb02ection is needed for the light to reach the cat?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33178\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-164.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 164\" width=\"193\" height=\"192\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-164.png 193w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-164-150x150.png 150w\" sizes=\"(max-width: 193px) 100vw, 193px\" \/><\/p>\n<p>Answer: The line of reflection will be y-axis.<\/p>\n<p><strong>2.3 Rotations<\/strong> (pp. 55\u201362)<\/p>\n<p><strong>Tell whether the blue \ufb01gure is a rotation of the red \ufb01gure about the origin. If so, give the angle and the direction of rotation.<\/strong><\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33179\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-165.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 165\" width=\"203\" height=\"155\" \/><\/p>\n<p>Answer:<br \/>\nThe answer is no because the blue figure is the mirror image of the red figure. The blue figure is the result of the reflection of red figure about the y-axis. Also, both red and blue figure are facing each other with the y-axis in the center of both which remains that it is not the case of rotation.<\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33180\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-166.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 166\" width=\"198\" height=\"156\" \/><\/p>\n<p>Answer:<br \/>\nThe answer is yes, because the red figure is in the 1st quadrant and the blue figure in third quadrant. Also, both blue and red figure are facing each other in opposite directions which blue figure is the result of the rotation of red figure.<br \/>\nWhen red figure is rotated 180 degrees counterclockwise it will result in a blue figure.<\/p>\n<p>The vertices of a triangle are A(-4, 2), B(-2, 2), and (-3, 4). Rotate the triangle as described. Find the coordinates of the image.<\/p>\n<p>Question 19.<br \/>\n180\u00b0 about the origin<\/p>\n<p>Answer:<br \/>\nWe know that when a point is rotated 180 degrees about origin then both x coordinate and y coordinate becomes opposite.<br \/>\nA(x, y) = A'(-x, -y)<br \/>\nGiven points: A(-4, 2), B(-2, 2), and C(-3, 4)<br \/>\nRotated 180 degrees about origin:<br \/>\nA(-4, 2) = A'(4, -2)<br \/>\nB(-2, 2) = B'(2, -2)<br \/>\nC(-3, 4) = C'(3, -4)<br \/>\nThe coordinate of the image are A'(4, -2), B'(2, -2), C'(3, -4)<\/p>\n<p>Question 20.<br \/>\n270\u00b0 clockwise about the origin<\/p>\n<p>Answer:<br \/>\nWe know that when a point is rotated 90 degrees counterclockwise about origin then both x coordinate and y coordinate becomes opposite.<br \/>\nP(x, y) = P'(-y, x)<br \/>\nGiven points: A(-4, 2), B(-2, 2), and C(-3, 4)<br \/>\nRotating 270 degrees clockwise about the origin:<br \/>\nA(-4, 2) = A'(-2, -4)<br \/>\nB(-2, 2) = B'(-2, -2)<br \/>\nC(-3, 4) = C'(-4, -3)<br \/>\nThe coordinate of the image are A'(-2, -4), B'(-2, -2), C'(-4, -3)<\/p>\n<p>Question 21.<br \/>\nA bicycle wheel is represented in a coordinate plane with the center of the wheel at the origin. Re\ufb02ectors are placed on the bicycle wheel at points (7, 4) and (-5, -6). After a bike ride, the re\ufb02ectors have rotated 90\u00b0 counterclockwise about the origin. What are the locations of the re\ufb02ectors at the end of the bike ride?<\/p>\n<p>Answer:<br \/>\nWe know that when a point is rotated 90 degrees counterclockwise about origin then both x coordinate and y coordinate becomes opposite.<br \/>\nP(x, y) = P'(-y, x)<br \/>\nRe\ufb02ectors are placed on the bicycle wheel at points (7, 4) and (-5, -6)<br \/>\nA(7, 4) = A'(-4, 7)<br \/>\nB(-5, -6) = B'(6, -5)<br \/>\nHence the new coordinate of the reflector are A'(-4, 7), B'(6, -5)<\/p>\n<p><strong>2.4 Congruent Figures<\/strong> (pp. 63\u201368)<\/p>\n<p><strong>Identify any congruent \ufb01gures in the coordinate plane.<\/strong><\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33181\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-167.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 167\" width=\"192\" height=\"191\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-167.png 192w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-167-150x150.png 150w\" sizes=\"(max-width: 192px) 100vw, 192px\" \/><\/p>\n<p>Answer:<br \/>\nAB = ED<br \/>\nBC = DC<br \/>\nCA = CE<br \/>\n\u2220A = \u2220E<br \/>\n\u2220B = \u2220D<br \/>\n\u2220C = \u2220C<br \/>\nWhen we see both triangles ABC and EDC closely we observe that both the triangles are the mirror images of each other with the y-axis as the line of reflection. So all the corresponding sides are equal and also all the corresponding angles, this means that both the triangle are congruent.<br \/>\nHence \u0394ABC is congruent to \u0394EDC<br \/>\nGH = JK<br \/>\nHF = KI<br \/>\nFG = IJ<br \/>\n\u2220G = \u2220J<br \/>\n\u2220H = \u2220K<br \/>\n\u2220F = \u2220I<br \/>\nSo we can see that all the corresponding sides are equal and also all the corresponding angles. this means that both the triangles are congruent.<br \/>\nHence \u0394GHF is congruent to \u0394JKI<\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33182\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-168.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 168\" width=\"195\" height=\"185\" \/><\/p>\n<p>Answer:<br \/>\nWhen we observe square ABCD and square EFGH we can see that<br \/>\nAB = EF<br \/>\nBC = FG<br \/>\nCD = GH<br \/>\nDA = HE<br \/>\n\u2220A = \u2220E<br \/>\n\u2220B = \u2220F<br \/>\n\u2220C = \u2220G<br \/>\n\u2220D = \u2220H<br \/>\nWe can see that all the corresponding sides are equal and also all the corresponding angles, this means that both are congruent.<br \/>\nRS = IJ<br \/>\nST = JK<br \/>\nTU = KL<br \/>\nUR = LI<br \/>\n\u2220R = \u2220I<br \/>\n\u2220S = \u2220J<br \/>\n\u2220T = \u2220K<br \/>\n\u2220L = \u2220U<br \/>\nHence rectangle RSTU is congruent to rectangle IJKL<\/p>\n<p><strong>The red \ufb01gure is congruent to the blue \ufb01gure. Describe a sequence of rigid motions between the \ufb01gures.<\/strong><\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33183\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-169.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 169\" width=\"199\" height=\"188\" \/><\/p>\n<p>Answer:<br \/>\nFirst, rotate the blue figure 90\u00b0 clockwise because the blue figure is in a vertical position but the red figure is in the horizontal position.<br \/>\nTranslate the image 5 units right because the first image formed after the rotation will in the second quadrant but the red figure in the first quadrant.<\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33184\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-170.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 170\" width=\"196\" height=\"192\" \/><\/p>\n<p>Answer:<br \/>\nFirst, reflect the blue figure about the y-axis because both red and blue figure is facing each other and they are the mirror image of each other.<br \/>\nThen translate the image 2 units up because the first image formed after reflection will be at the same distance from the x-axis but the red figure is touchung the x-axis.<\/p>\n<p>Question 26.<br \/>\nThe \ufb01gures are congruent. Name the corresponding angles and the corresponding sides.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33185\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-171.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 171\" width=\"271\" height=\"79\" \/><\/p>\n<p>Answer:<br \/>\nCorresponding sides are<br \/>\nAB = KL<br \/>\nBC = LM<br \/>\nCA = MK<br \/>\nCorresponding angles<br \/>\n\u2220A = \u2220K<br \/>\n\u2220B = \u2220L<br \/>\n\u2220C = \u2220M<\/p>\n<p>Question 27.<br \/>\nTrapezoids EFGH and QRST are congruent.<br \/>\na. What is the length of side QR ?<\/p>\n<p>Answer:<br \/>\nLength of side:<br \/>\nQR = EF = 3 feet<\/p>\n<p>b. Which angle in QRST corresponds to \u2220H?<br \/>\nAnswer:<br \/>\nThe angle that corresponds to \u2220H is \u2220T<\/p>\n<p>c. What is the perimeter of QRST ?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33186\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-172.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 172\" width=\"348\" height=\"87\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-172.png 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-172-300x75.png 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Answer:<br \/>\nPerimeter of QSRT = QR + RS + ST + TQ<br \/>\n= EF + FG + GH + HE<br \/>\n= 3 + 5 + 4 + 8<br \/>\n= 20 ft<\/p>\n<p><strong>2.5 Dilations<\/strong> (pp. 69\u201376)<\/p>\n<p><strong>Tell whether the blue \ufb01gure is a dilation of the red \ufb01gure.<\/strong><\/p>\n<p>Question 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33187\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-173.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 173\" width=\"166\" height=\"79\" \/><\/p>\n<p>Answer:<br \/>\nThe answer is no because dilation the size of the image either increases or decreases that depend on the type of dilation. We can see that both the red and blue figure are of the same size which means that the blue figure is not dilation of the red figure.<\/p>\n<p>Question 29.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33188\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-174.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 174\" width=\"159\" height=\"100\" \/><\/p>\n<p>Answer:<br \/>\nThe answer is yes because both red and blue figures are of the same shape and all the corresponding angles are equal but the blue figure is larger than the red figure. And in dilation, the size of the image is either increases or decreases but the shape always remains the same. So blue figure is the result of dilation of red figure.<\/p>\n<p><strong>The vertices of a \ufb01gure are given. Draw the \ufb01gure and its image after a dilation with the given scale factor. Identify the type of dilation.<\/strong><\/p>\n<p>Question 30.<br \/>\nP(-3, -2), Q(-3, 0), R(0, 0); k = 4<\/p>\n<p>Answer:<br \/>\nA(x, y) = A'(x . a, y . a)<br \/>\nWhere a is the scaling factor<br \/>\nGiven,<br \/>\nP(-3, -2), Q(-3, 0), R(0, 0); k = 4<br \/>\nP(-3, -2) = P'(-3 . 4, -2 . 4) = P'(-12, -8)<br \/>\nQ(-3, 0) = Q'(-3 . 4, 0 . 4) = Q'(-12, 0)<br \/>\nR(0, 0) = R'(0 . 4, 0 . 4) = R'(0, 0)<br \/>\nThus the coordinates of the image: P'(-12, -8), Q'(-12, 0), R'(0, 0)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-51804\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answer-Key-for-Grade-8-Chapter-2-img_45-300x183.png\" alt=\"Bigideas Math Answer Key for Grade 8 Chapter 2 img_45\" width=\"300\" height=\"183\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answer-Key-for-Grade-8-Chapter-2-img_45-300x183.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answer-Key-for-Grade-8-Chapter-2-img_45.png 617w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 31.<br \/>\nB(3, 3), C(3, 6), D(6, 6), E(6, 3); k = \\(\\frac{1}{3}\\)<\/p>\n<p>Answer:<br \/>\nA(x, y) = A'(x . a, y . a)<br \/>\nWhere a is the scaling factor<br \/>\nGiven,<br \/>\nB(3, 3), C(3, 6), D(6, 6), E(6, 3); k = \\(\\frac{1}{3}\\)<br \/>\nB(3, 3) = B'(3 . \\(\\frac{1}{3}\\), 3 . \\(\\frac{1}{3}\\)) = B'(1, 1)<br \/>\nC(3, 6) = C'(3 . \\(\\frac{1}{3}\\), 6 . \\(\\frac{1}{3}\\)) = C'(1, 2)<br \/>\nD(6, 6) = D'(6 . \\(\\frac{1}{3}\\), 6 . \\(\\frac{1}{3}\\)) = D'(2, 2)<br \/>\nE(6, 3) = E'(6 . \\(\\frac{1}{3}\\), 3 . \\(\\frac{1}{3}\\)) = E'(2, 1)<br \/>\nThus the coordinates of the image: B'(1, 1), C'(1, 2), D'(2, 2), E'(2, 1)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-51807\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIm-Grade-8-Chapter-2-Answers-img_46-300x277.png\" alt=\"BIm Grade 8 Chapter 2 Answers img_46\" width=\"300\" height=\"277\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIm-Grade-8-Chapter-2-Answers-img_46-300x277.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIm-Grade-8-Chapter-2-Answers-img_46.png 602w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 32.<br \/>\nThe blue \ufb01gure is a dilation of the red \ufb01gure. Identify the type of dilation and \ufb01nd the scale factor.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33190\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-175.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 175\" width=\"163\" height=\"162\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-175.png 163w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-175-150x150.png 150w\" sizes=\"(max-width: 163px) 100vw, 163px\" \/><\/p>\n<p>Answer:<br \/>\nAB = 1 unit<br \/>\nA&#8217;B&#8217; = 2 units<br \/>\nscale factor = size of image figure\/size of actual figure<br \/>\nscale factor = 2\/1 = 2<br \/>\nWe can see from the above figure that the size of the image figure are larger as compared to the size of the original image so it is the Enlargement dilation.<\/p>\n<p>Question 33.<br \/>\nThe vertices of a rectangle are Q(-6, 2), R(6, 2), S(6, -4), and T(-6, -4). Dilate the rectangle with respect to the origin using a scale factor of \\(\\frac{3}{2}\\). Then translate it 5 units right and 1 unit down. What are the coordinates of the image?<\/p>\n<p>Answer:<br \/>\nWhen the points of given figure are dilated we simply multiply each x and y coordinate by the given scale factor.<br \/>\nP(x, y) = P'(x . a, y . a)<br \/>\nGiven points of the rectangle: Q(-6, 2), R(6, 2), S(6, -4), and T(-6, -4), scale factor = \\(\\frac{3}{2}\\)<br \/>\nQ(-6, 2) = Q'(-6 . \\(\\frac{3}{2}\\), 2 . \\(\\frac{3}{2}\\)) = Q'(-9, 3)<br \/>\nR(6, 2) = R'(6 . \\(\\frac{3}{2}\\), 2 . \\(\\frac{3}{2}\\)) = R'(9, 3)<br \/>\nS(6, -4) = S'(6 . \\(\\frac{3}{2}\\), -4 . \\(\\frac{3}{2}\\)) = S'(9, 6)<br \/>\nT(-6, -4) = T'(-6 . \\(\\frac{3}{2}\\), -4 . \\(\\frac{3}{2}\\)) = T'(-9, -6)<br \/>\nThus the coordinates of the image: Q'(-9, 3), R'(9, 3), S'(9, 6), T'(-9, -6)<br \/>\nQ'(-9, 3), R'(9, 3), S'(9, 6), T'(-9, -6) a = 5, b = -1<br \/>\nQ&#8221;(-9 + a, 3 + b) = Q&#8221;(-9 + 5, 3 &#8211; 1) = Q&#8221;(-4, 2)<br \/>\nR&#8221;(9 + a, 3 + b) = R&#8221;(9 + 5, 3 &#8211; 1) = R&#8221;(14, 2)<br \/>\nS&#8221;(9 + a, -6 + b) = S&#8221;(9 + 5, -6 &#8211; 1) = S&#8221;(14, -7)<br \/>\nT&#8221;(-9 + a, -6 + b) = T&#8221;(-9 + 5, -6 &#8211; 1) = T&#8221;(-4, -7)<br \/>\nThus the coordinates of the image: Q&#8221;(-4, 2), R&#8221;(14, 2), S&#8221;(14, -7), T&#8221;(-4, -7)<\/p>\n<p><strong>2.6 Similar Figures<\/strong><\/p>\n<p>Question 34.<br \/>\nDetermine whether the two \ufb01gures are similar. Explain your reasoning.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-33189\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-175.1.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 175.1\" width=\"198\" height=\"192\" \/><\/p>\n<p>Answer:<br \/>\nNo, the above two figures are not similar.<\/p>\n<p>Question 35.<br \/>\nDraw \ufb01gures with the given vertices in a coordinate plane. Which \ufb01gures are similar? Explain your reasoning.<br \/>\nTriangle A: (-4, 4), (-2, 4), (-2, 0)<br \/>\nTriangle B: (-2, 2), (-1, 2), (-1, 0)<br \/>\nTriangle C: (6, 6), (3, 6), (3, 0)<\/p>\n<p>Answer:<br \/>\nTriangle A: (-4, 4), (-2, 4), (-2, 0)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-51812\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Ch-2-img_48-260x300.png\" alt=\"BIM Grade 8 Solution Key Ch 2 img_48\" width=\"260\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Ch-2-img_48-260x300.png 260w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Ch-2-img_48.png 361w\" sizes=\"(max-width: 260px) 100vw, 260px\" \/><br \/>\nTriangle B: (-2, 2), (-1, 2), (-1, 0)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-51813\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-Grade-8-Ch-2-img_49-284x300.png\" alt=\"Bigideas Math Answers Grade 8 Ch 2 img_49\" width=\"284\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-Grade-8-Ch-2-img_49-284x300.png 284w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-Grade-8-Ch-2-img_49.png 361w\" sizes=\"(max-width: 284px) 100vw, 284px\" \/><br \/>\nTriangle C: (6, 6), (3, 6), (3, 0)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-51814\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Answers-for-Grade-8-Chapter-2-img_50-300x284.png\" alt=\"BIM Answers for Grade 8 Chapter 2 img_50\" width=\"300\" height=\"284\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Answers-for-Grade-8-Chapter-2-img_50-300x284.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Answers-for-Grade-8-Chapter-2-img_50.png 522w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>The \ufb01gures are similar. Find x.<\/p>\n<p>Question 36.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33191\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-177.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 177\" width=\"229\" height=\"91\" \/><\/p>\n<p>Answer:<br \/>\nRatio of sides of larger triangle = Ratio of sides of smaller triangle<br \/>\n20\/14 = x\/7<br \/>\nx = 10<br \/>\nThus the value of x is 7 inches.<\/p>\n<p>Question 37.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33192\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-178.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 178\" width=\"204\" height=\"114\" \/><\/p>\n<p>Answer:<br \/>\nRatio of sides of larger parallelogram= Ratio of sides of smaller parallelogram<br \/>\nx\/6 = 6\/4<br \/>\nx = 9<br \/>\nThus the value of x is 9 cm<\/p>\n<p><strong>2.7 Perimeters and Areas of Similar Figures<\/strong> (pp. 83-88)<\/p>\n<p><strong>Find the values of the ratios (red to blue) of the perimeters and areas of the similar \ufb01gures.<\/strong><\/p>\n<p>Question 38.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33267\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-2-Transformations-179.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 2 Transformations 179\" width=\"209\" height=\"78\" \/><\/p>\n<p>Answer:<br \/>\nPerimeter of figure A\/Perimeter of figure B = Side length of figure A\/Side length of figure B<br \/>\nPerimeter of red figure\/Perimeter of blue figure = 6\/8 = 3\/4<br \/>\nHence the ratio of perimeter of red triangle to blue is 3\/4<br \/>\nArea of figure A\/Area of figure B = (Side length of A\/Side length of B)\u00b2<br \/>\nArea of red figure\/Area of blue figure = (6\/8)\u00b2 = 9\/16<br \/>\nThus the ratio of the perimeter of the red to the blue triangle is 9\/16<\/p>\n<p>Question 39.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33193\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-180.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 180\" width=\"275\" height=\"97\" \/><\/p>\n<p>Answer:<br \/>\nPerimeter of figure A\/Perimeter of figure B = Side length of figure A\/Side length of figure B<br \/>\nPerimeter of red figure\/Perimeter of blue figure = 28\/16 = 7\/4<br \/>\nHence the ratio of the perimeter of red rectangle to blue is 7\/4<br \/>\nArea of figure A\/Area of figure B = (Side length of A\/Side length of B)\u00b2<br \/>\nArea of red figure\/Area of blue figure = (28\/16)\u00b2 = 49\/16<br \/>\nThus the ratio of the perimeter of the red to the blue rectangle is 49\/16<\/p>\n<p><strong>The \ufb01gures are similar. Find x.<\/strong><\/p>\n<p>Question 40.<br \/>\nThe ratio of the perimeters is 5 :7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33194\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-181.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 181\" width=\"238\" height=\"152\" \/><\/p>\n<p>Answer:<br \/>\n5\/7 = 12\/x<br \/>\nx =(12 \u00d7 7)\/5<br \/>\nx = 16.8 cm<br \/>\nThus the value of x is 16.8 cm<\/p>\n<p>Question 41.<br \/>\nThe ratio of the perimeters is 6 : 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33195\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-182.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 182\" width=\"232\" height=\"140\" \/><\/p>\n<p>Answer:<br \/>\n6\/5 = x\/6<br \/>\nx = 36\/5<br \/>\nx = 7.2<br \/>\nThus the value of x is 7.2<\/p>\n<p>Question 42.<br \/>\nTwo photos are similar. The ratio of the corresponding side lengths is 3 : 4. What is the ratio of the areas?<\/p>\n<p>Answer:<br \/>\nArea of photo A\/Area of photo B = (Side length of photo A\/Side length of photo B)\u00b2<br \/>\nArea of photo A\/Area of photo B = (3\/4)\u00b2 = 9\/16<br \/>\nThus the ratio of the area of two photos is 9\/16<\/p>\n<p>Question 43.<br \/>\nThe ratio of side lengths of Square A to Square B is 2 : 3. The perimeter of Square A is 16 inches. What is the area of Square B?<\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nThe ratio of side lengths of Square A to Square B is 2 : 3.<br \/>\nThe perimeter of Square A is 16 inches.<br \/>\nPerimeter of Square A\/Perimeter of Square B = Side length of Square A\/Side length of Square B<br \/>\nThe perimeter of Square B = (16 \u00d7 3)\/2<br \/>\nThe perimeter of Square B = 24 inches<br \/>\nSide length of square B = Perimeter\/4 = 24\/4 = 6 inch<br \/>\nArea of square B = s \u00d7 s = 6 \u00d7 6 = 36 sq. in<\/p>\n<p>Question 44.<br \/>\nThe TV screen is similar to the computer screen. What is the area of the TV screen?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33197\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-183.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 183\" width=\"346\" height=\"191\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-183.png 346w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-183-300x166.png 300w\" sizes=\"(max-width: 346px) 100vw, 346px\" \/><\/p>\n<p>Answer:<br \/>\nArea of computer screen = 108 sq. in<br \/>\nThe side length of the computer screen = 12 in<br \/>\nThe side length of the TV screen = 20 in<br \/>\nArea of TV screen = (25 \u00d7 108)\/9<br \/>\nArea of TV screen = 300 sq. in<br \/>\nHence the area of the TV screen is 300 sq. in<\/p>\n<h3><a id=\"Transformations_Practice_Test\"><\/a>Transformations Practice Test<\/h3>\n<p><strong>2 Practice Test<\/strong><\/p>\n<p><strong>Triangles ABC and DEF are congruent.<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-33196\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-183.1.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 183.1\" width=\"244\" height=\"115\" \/><\/p>\n<p>Question 1.<br \/>\nWhich angle of DEF corresponds to \u2220C ?<\/p>\n<p>Answer:<br \/>\nCorresponding sides<br \/>\nSide AB = Side DE<br \/>\nSide BC = Side EF<br \/>\nSide CA = Side ED<br \/>\nCorresponding angles<br \/>\n\u2220A = \u2220D<br \/>\n\u2220B = \u2220E<br \/>\n\u2220C = \u2220F<br \/>\nThus the angle correspond to \u2220C is \u2220F<\/p>\n<p>Question 2.<br \/>\nWhat is the perimeter of DEF ?<\/p>\n<p>Answer:<br \/>\nCorresponding sides<br \/>\nSide AB = Side DE<br \/>\nSide BC = Side EF<br \/>\nSide CA = Side ED<br \/>\nCorresponding angles<br \/>\n\u2220A = \u2220D<br \/>\n\u2220B = \u2220E<br \/>\n\u2220C = \u2220F<br \/>\nPerimeter of DEF = DE + EF + FD<br \/>\n= AB + BC + CA<br \/>\n= 5 + 4 + 6<br \/>\n= 15 cm<br \/>\nThus the perimeter of the \u0394DEF is 15 cm<\/p>\n<p><strong>Tell whether the blue \ufb01gure is a translation, re\ufb02ection, rotation, or dilation of the red \ufb01gure.<\/strong><\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33198\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-184.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 184\" width=\"219\" height=\"120\" \/><\/p>\n<p>Answer: The scale factor of a dilation is greater than 1 because the shape of the blue figure is larger than the red figure.<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33199\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-185.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 185\" width=\"228\" height=\"93\" \/><\/p>\n<p>Answer:<br \/>\nThe blue figure is the reflection of the red figure. Because the blue figure is the mirror image of red figure. Also, the shape and size of both red and blue figures are the same.<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33200\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-186.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 186\" width=\"233\" height=\"96\" \/><\/p>\n<p>Answer:<br \/>\nThe blue figure is the translation of the red figure. Because the shape and size of both red and blue figures are the same. And both the figure is not facing to each other. This means that the blue figure is the result of the translation of the red figure.<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33201\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-187.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 187\" width=\"201\" height=\"120\" \/><\/p>\n<p>Answer:<br \/>\nThe blue figure is the result of the rotation of the red figure. Because the shape and size of both the red and blue figure are the same but the figure is horizontal and the blue figure is vertical. This means that the blue figure is the result of the rotation of the term figure.<\/p>\n<p><strong>The vertices of a triangle are A(2, 5), B(1, 2), and C(3, 1). Find the coordinates of the image after the transformations given.<\/strong><\/p>\n<p>Question 7.<br \/>\nRe\ufb02ect in the y-axis.<\/p>\n<p>Answer:<br \/>\nA(x, y) = A'(-x, y)<br \/>\nA(2, 5), B(1, 2), C(3, 1)<br \/>\nReflection about the y-axis:<br \/>\nA(2, 5) = A'(-2, 5)<br \/>\nB(1, 2) = B'(-1, 2)<br \/>\nC(3, 1) = C'(-3, 1)<br \/>\nThus the coordinates of the image: A'(-2, 5), B'(-1, 2), C'(-3, 1)<\/p>\n<p>Question 8.<br \/>\nRotate 90\u00b0 clockwise about the origin.<\/p>\n<p>Answer:<br \/>\nA(x, y) = A'(x, -y)<br \/>\nGiven, A(2, 5), B(1, 2), C(3, 1)<br \/>\nA(2, 5) = A'(2, -5)<br \/>\nB(1, 2) = B'(1, -2)<br \/>\nC(3, 1) = C'(3, -1)<br \/>\nThus the coordinates of the image: A'(2, -5), B'(1, -2), C'(3, -1)<\/p>\n<p>Question 9.<br \/>\nRe\ufb02ect in the x-axis, and then rotate 90\u00b0 counterclockwise about the origin.<\/p>\n<p>Answer:<br \/>\nA(x, y) = A'(x, -y)<br \/>\nGiven, A(2, 5), B(1, 2), C(3, 1)<br \/>\nA(2, 5) = A'(2, -5)<br \/>\nB(1, 2) = B'(1, -2)<br \/>\nC(3, 1) = C'(3, -1)<br \/>\nThus the coordinates of the image: A'(2, -5), B'(1, -2), C'(3, -1)<br \/>\nA'(2, -5) = A&#8221;(2, 5)<br \/>\nB'(1, -2) = B&#8221;(1, 2)<br \/>\nC'(3, -1) = C&#8221;(3, 1)<br \/>\nThus the coordinates of the image: A&#8221;(2, 5), B&#8221;(1, 2), C&#8221;(3, 1)<\/p>\n<p>Question 10.<br \/>\nDilate with respect to the origin using a scale factor of 2. Then translate 2 units left and 1 unit up.<\/p>\n<p>Answer:<br \/>\nWhen the points of given figure are dilated we simply multiply each x and y coordinate by the given scale factor.<br \/>\nP(x, y) = P'(x . a, y . a)<br \/>\nGiven points of the triangle: A(2, 5), B(1, 2), C(3, 1) and scale factor = 2<br \/>\nDilating the figure by scale factor of 2<br \/>\nA (2, 5) = A'(2 . 2, 5 . 2) = A'(4, 10)<br \/>\nB (1, 2) = B'(1 . 2, 2 . 2) = B'(2, 4)<br \/>\nC (3, 1) = C'(3 . 2, 1 . 2) =\u00a0 C'(6, 2)<br \/>\nHence the coordinates of the image are A'(4, 10), B'(2, 4),\u00a0 C'(6, 2)<br \/>\nNow translating image 2 unit left and 1 unit up.<br \/>\nGiven: A'(4, 10), B'(2, 4),\u00a0 C'(6, 2) a = -2, b = 1<br \/>\nA&#8221;(4 + a, 10 + b) = A&#8221;(4 &#8211; 2, 10 + 1) = A&#8221;(2, 11)<br \/>\nB&#8221;(2 + a, 4 + b) = B&#8221;(2 &#8211; 2, 4 + 1) = B&#8221;(0, 5)<br \/>\nC&#8221;(6 + a, 2 + b) = C&#8221;(6 &#8211; 2, 2 + 1) = C&#8221;(4, 3)<br \/>\nHence the coordinates of the image are A&#8221;(2, 11), B&#8221;(0, 5), C&#8221;(4, 3)<\/p>\n<p>Question 11.<br \/>\nIn a coordinate plane, draw Rectangle A: (-4, 4), (0, 4), (0, 2), (-4, 2); Rectangle B: (-2, 2), (0, 2), (0, 1), (-2, 1); and Rectangle C:(-6, 6), (0, 6), (0, 3), (-6, 3). Which \ufb01gures are similar? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nRectangle A: (-4, 4), (0, 4), (0, 2), (-4, 2)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-51826\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Chapter-2-Solutions-img_51-300x245.png\" alt=\"BIM Grade 8 Chapter 2 Solutions img_51\" width=\"300\" height=\"245\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Chapter-2-Solutions-img_51-300x245.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Chapter-2-Solutions-img_51.png 478w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nRectangle B: (-2, 2), (0, 2), (0, 1), (-2, 1)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-51827\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Chapter-2-Solutions-img_52-300x248.png\" alt=\"BIM Grade 8 Chapter 2 Solutions img_52\" width=\"300\" height=\"248\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Chapter-2-Solutions-img_52-300x248.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Chapter-2-Solutions-img_52.png 409w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nRectangle C:(-6, 6), (0, 6), (0, 3), (-6, 3)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-51828\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Chapter-2-Solutions-img_53-300x243.png\" alt=\"BIM Grade 8 Chapter 2 Solutions img_53\" width=\"300\" height=\"243\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Chapter-2-Solutions-img_53-300x243.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Chapter-2-Solutions-img_53.png 465w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 12.<br \/>\nTranslate a point (x, y) 3 units left and 5 units up. Then translate the image 5 units right and 2 units up. What are the coordinates of the point after the translations?<\/p>\n<p>Answer:<br \/>\nWe know that to translate a figure &#8216;a&#8217; units horizontally and &#8216;b&#8217; units vertically in the coordinate plane, &#8216;a&#8217; is added to x-coordinate and &#8216;b&#8217; is added to the y-coordinate of the vertices.<br \/>\nA(x,y) = A'(x+a, y+b)<br \/>\nThe value a and b will be positive if the shift is Right and Vertical Up and the value of a and b will be negative if the shift is left and vertical Down.<br \/>\nGiven: A(x,y) and a = -3, b = 5<br \/>\nA'(x+a, y+b) = A'(x &#8211; 3, y + 5)<br \/>\nNow translating image 5 units right and 2 units up.<br \/>\nImage after first translation: A'(x &#8211; 3, y + 5) and a = 5, b = 2<br \/>\nA&#8221;(x &#8211; 3 + a, y + 5 + b) = A&#8221;(x &#8211; 3 + 5, y + 5 + 2) = A&#8221;(x + 2, y + 7)<br \/>\nThus the final image will be A&#8221;(x + 2, y + 7)<\/p>\n<p>Question 13.<br \/>\nThe two \ufb01gures are similar.<br \/>\n(a) Find the value of x.<\/p>\n<p>Answer:<br \/>\nRatio of sides of red figure = Ratio of sides of blue figure<br \/>\nx\/14 = 10\/8<br \/>\nx = (10 \u00d7 14)\/8<br \/>\nx = 17.5<\/p>\n<p>(b) Find the values of the ratios (red to blue) of the perimeters and of the areas.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33202\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-188.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 188\" width=\"196\" height=\"97\" \/><\/p>\n<p>Answer:<br \/>\nPerimeter of red figure\/Perimeter of blue figure = Side length of red figure\/Side length of blue figure<br \/>\nPerimeter of red figure\/Perimeter of blue figure = 14\/8 = 7\/4<br \/>\nThus the ratio of the perimeter of red to blue figure is 7\/4<br \/>\nArea of red figure\/Area of blue figure = (side length of red figure\/side length of blue figure)\u00b2<br \/>\nArea of red figure\/Area of blue figure = (14\/8)\u00b2 = 49\/16<br \/>\nThus the ratio of the perimeter of red to blue triangle is 49\/16<\/p>\n<p>Question 14.<br \/>\nA wide-screen television measures 36 inches by 54 inches. A movie theater screen measures 42 feet by 63 feet. Are the screens similar? Explain.<\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nA wide-screen television measures 36\/54 = 2\/3<br \/>\nA movie theater screen measures 42\/63 = 2\/3<br \/>\nWe can see that the ratio of corresponding sides of the television screen is equal to the ratio of corresponding sides of the movie theatre. So television screens and movie theatres are similar.<\/p>\n<p>Question 15.<br \/>\nYou want to use the rectangular piece of fabric shown to make a pair of curtains for your window. Name the types of congruent shapes you can make with one straight cut. Draw an example of each type.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33203\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-189.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 189\" width=\"277\" height=\"119\" \/><\/p>\n<p>Answer:<br \/>\nThe types of congruent shapes that can be made with one straight cut<br \/>\n2 right triangles<br \/>\n2 rectangles<br \/>\n2 right trapezoid<\/p>\n<h3><a id=\"Transformations_Cumulative_Practice\"><\/a>Transformations Cumulative Practice<\/h3>\n<p><strong>Cumulative Practice<\/strong><\/p>\n<p>Question 1.<br \/>\nA clockwise rotation of 90\u00b0 is equivalent to a counterclockwise rotation of how many degrees?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33204\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-190.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 190\" width=\"80\" height=\"68\" \/><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-33206\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-191.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 191\" width=\"370\" height=\"424\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-191.png 370w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-191-262x300.png 262w\" sizes=\"(max-width: 370px) 100vw, 370px\" \/><\/p>\n<p>Answer:<br \/>\n90\u00b0 of clockwise rotation = (360 &#8211; 90)\u00b0 of counterclockwise rotation<br \/>\n= 270\u00b0 of counterclockwise rotation<\/p>\n<p>Question 2.<br \/>\nThe formula K = C + 273.15 converts temperatures from degrees Celsius C to Kelvin K. Which of the following formulas is not correct?<br \/>\nA. K &#8211; C = 273.<br \/>\nB. C = K &#8211; 273.15<br \/>\nC. C &#8211; K = -273.15<br \/>\nD. C = K + 273.15<\/p>\n<p>Answer: C = K + 273.15<\/p>\n<p>Question 3.<br \/>\nYou want to solve the equation -3(x + 2) = 12x. What should you do \ufb01rst?<br \/>\nF. Subtract 2 from each side.<br \/>\nG. Add 3 to each side.<br \/>\nH. Multiply each side by -3.<br \/>\nI. Divide each side by -3.<\/p>\n<p>Answer: I. Divide each side by -3.<\/p>\n<p>Explanation:<br \/>\n-3(x + 2) = 12x<br \/>\nx + 2 = -4x<br \/>\nx = -4x &#8211; 2<br \/>\nx + 4x = -2<br \/>\n5x = -2<br \/>\nx = &#8211;\\(\\frac{2}{5}\\)<br \/>\nThus the correct answer is option I.<\/p>\n<p>Question 4.<br \/>\nWhich value of x makes the equation \\(\\frac{3}{4} x\\) = 12 true?<br \/>\nA. 9<br \/>\nB. 11\\(\\frac{1}{4}\\)<br \/>\nC. 16<br \/>\nD. 48<\/p>\n<p>Answer: C. 16<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{3}{4} x\\) = 12<br \/>\n3x = 12 \u00d7 4<br \/>\n3x = 48<br \/>\nx = \\(\\frac{48}{3}\\)<br \/>\nx = 16<br \/>\nThus the correct answer is option C.<\/p>\n<p>Question 5.<br \/>\nA triangle is graphed in the coordinate plane. What are the coordinates of the image after a translation 3 units right and 2 units down?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33205\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-191.1.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 191.1\" width=\"199\" height=\"194\" \/><br \/>\nF. A'(1, 4), B'(1, 1), C'(3, 1)<br \/>\nG. A'(1, 2), B'(1, -1), C'(3, -1)<br \/>\nH. A'(-2, 2), B'(-2, -1), C'(0, -1)<br \/>\nI. A'(0, 1), B'(0, -2), C'(2, -2)<\/p>\n<p>Answer:<br \/>\nWe know that to translate a figure &#8216;a&#8217; units horizontally and &#8216;b&#8217; units vertically in the coordinate plane, &#8216;a&#8217; is added to x-coordinate and &#8216;b&#8217; is added to the y-coordinate of the vertices.<br \/>\nA(x,y) = A'(x+a, y+b)<br \/>\nThe value a and b will be positive if the shift is Right and Vertical Up and the value of a and b will be negative if the shift is left and vertical Down.<br \/>\nA(-2, 4), B(-2, 1), C(0, 1) and a = 3, b = -2<br \/>\nA'(-2+a, 4+b) = A'(-2 + 3, 4 &#8211; 2) = A'(1, 2)<br \/>\nB'(-2+a, 1+b) = B'(-2 + 3, 1 &#8211; 2) = B'(1,-1)<br \/>\nC'(0+a, 1+b) = C'(0 + 3, 1 &#8211; 2) = C'(3, -1)<br \/>\nCoordinate of the image are: A'(1, 2), B'(1,-1), C'(3, -1)<br \/>\nThus the correct answer is option G.<\/p>\n<p>Question 6.<br \/>\nYour friend solved the equation in the box shown. What should your friend do to correct the error that he made?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33207\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-192.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 192\" width=\"234\" height=\"260\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33208\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-193.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 193\" width=\"341\" height=\"199\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-193.png 341w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-193-300x175.png 300w\" sizes=\"(max-width: 341px) 100vw, 341px\" \/><\/p>\n<p>Answer:<br \/>\n&#8211;\\(\\frac{x}{3}\\) + \\(\\frac{2}{5}\\) = &#8211;\\(\\frac{7}{15}\\)<br \/>\n&#8211;\\(\\frac{x}{3}\\) = &#8211;\\(\\frac{13}{15}\\)<br \/>\nx = 2\\(\\frac{3}{5}\\)<br \/>\nThus the correct answer is option C.<\/p>\n<p>Question 7.<br \/>\nYour teacher dilates the rectangle using a scale factor of \\(\\frac{1}{2}\\).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33209\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-194.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 194\" width=\"372\" height=\"139\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-194.png 372w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-194-300x112.png 300w\" sizes=\"(max-width: 372px) 100vw, 372px\" \/><br \/>\nWhat is the area of the dilated rectangle in square inches?<\/p>\n<p>Answer:<br \/>\nl = 10 in<br \/>\nb = 6 in<br \/>\nscale factor = \\(\\frac{1}{2}\\)<br \/>\nNew length after dilation = 10 \u00d7 \\(\\frac{1}{2}\\) = 5<br \/>\nNew breadth after dilation = 6 \u00d7 \\(\\frac{1}{2}\\) = 3<br \/>\nArea of rectangle = l \u00d7 b<br \/>\nA = 5 \u00d7 3 = 15 sq. in<br \/>\nThe area of the dilated rectangle will be 5 in\u00b2<\/p>\n<p>Question 8.<br \/>\nYour cousin earns $9.25 an hour at work. Last week she earned $222.00 How many hours did she work last week?<br \/>\nF. \\(\\frac{1}{24}\\)<br \/>\nG. 22 hours<br \/>\nH. 24 hours<br \/>\nI. 212.75 hours<\/p>\n<p>Answer: H. 24 hours<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nYour cousin earns $9.25 an hour at work.<br \/>\nLast week she earned $222.00<br \/>\nTotal no. of working hour = total earning of week\/rate of one hour<br \/>\n= \\(\\frac{222}{9.25}\\)<br \/>\n= 24 hours<br \/>\nThus the correct answer is option H.<\/p>\n<p>Question 9.<br \/>\nTriangle EFG is a dilation of Triangle HIJ. Which proportion is not true for Triangle EFG and Triangle HIJ ?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33210\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-195.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 195\" width=\"319\" height=\"119\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-195.png 319w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-195-300x112.png 300w\" sizes=\"(max-width: 319px) 100vw, 319px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33211\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-196.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 196\" width=\"433\" height=\"107\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-196.png 433w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-196-300x74.png 300w\" sizes=\"(max-width: 433px) 100vw, 433px\" \/><\/p>\n<p>Answer: \\(\\frac{EG}{HI}\\) = \\(\\frac{FG}{IJ}\\)<br \/>\nThe correct answer is option B.<\/p>\n<p>Question 10.<br \/>\nThe red \ufb01gure is congruent to the blue \ufb01gure. Which of the following is a sequence of rigid motions between the \ufb01gures?<br \/>\nF. Re\ufb02ect the red triangle in the x-axis, and then translate it 3 units left.<br \/>\nG. Re\ufb02ect the red triangle in the x-axis, and then translate it 3 units right.<br \/>\nH. Re\ufb02ect the red triangle in the y-axis, and then translate it 3 units left.<br \/>\nI. Rotate the red triangle 90\u00b0 clockwise about the origin.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33212\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-197.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 197\" width=\"197\" height=\"205\" \/><\/p>\n<p>Answer:<br \/>\n1. First red triangle is reflected about the x-axis because both red and blue triangles are the mirror image of each other and also the red triangle is in the 1st quadrant and the blue triangle is in 4th quadrant.<br \/>\n2. Then translate the image 3 unit left because the base of both red and blue triangles is not opposite to each other.<br \/>\nThus the correct answer is option F.<\/p>\n<p>Question 11.<br \/>\nSeveral transformations are used to create the pattern.<br \/>\n<strong>Part A<\/strong><br \/>\nDescribe the transformation of Triangle GLM to Triangle DGH<\/p>\n<p>Answer:<br \/>\nBoth \u0394GLM and \u0394 DGH are of the same shape and size but their position are different so the transformation will be translated.<\/p>\n<p><strong>Part B<\/strong><br \/>\nDescribe the transformation of Triangle ALQ to Triangle GLM.<\/p>\n<p>Answer:<br \/>\nThe size of the triangle ALQ is four times the size of triangle GLM and the shape of both triangles is the same so the transformation will be dilation.<\/p>\n<p><strong>Part C<\/strong><br \/>\nTriangle DFN is a dilation of Triangle GHM. Find the scale factor.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33214\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-198.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 198\" width=\"75\" height=\"65\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33213\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-198.1.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 198.1\" width=\"231\" height=\"266\" \/><\/p>\n<p>Answer:<br \/>\nThe size of the triangle DFN is double the size of triangle GHM. So the scale factor of dilation will be 2.<\/p>\n<p>Question 12.<br \/>\nA rectangle is graphed in the coordinate plane.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33215\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-2-Transformations-199.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 2 Transformations 199\" width=\"197\" height=\"193\" \/><br \/>\nWhat are the coordinates of the image after a re\ufb02ection in the y-axis?<br \/>\nA. J'(4, 1), K'(4, 3), L'( 1, 3), M'(-1, 1)<br \/>\nB. J'(-4, 1), K(-4, -3), L'(1, -3), M'(1, 1)<br \/>\nC. J'(1, 4), K'(3, 4), L'(3, -1), M'(1, -1)<br \/>\nD. J'(-4, 1), K'(-4, 3), L'(1, 3), M'(1, 1)<\/p>\n<p>Answer:<br \/>\nWe know that when a point is reflected about the y-axis then the x-coordinate becomes the opposite.<br \/>\nA(x, y) = A'(-x, y)<br \/>\nJ(-4, 1), K(-4, 3), L(1, 3), M(1, 1)<br \/>\nReflection about the y-axis:<br \/>\nJ(-4, 1) = J'(4, 1)<br \/>\nK(-4, 3) = K'(4, 3)<br \/>\nL(1, 3) = L'(-1, 3)<br \/>\nM(1, 1) = M'(-1, 1)<br \/>\nCoordinate of image are: J'(4, 1), K'(4, 3), L'(-1, 3), M'(-1, 1)<br \/>\nThus the correct answer is option A.<\/p>\n<p><em>Conclusion:<\/em><\/p>\n<p>I wish the information provided in the above article regarding the Big Ideas Math Grade 8 Chapter 2 Transformations Answer Key is beneficial for all middle school students. Make use of the given links and score good marks in the exams. Share this pdf with your friends and help them to overcome the difficulties in maths. And also bookmark our page to get the latest updates of all Big Ideas Math Grade 8 Answers.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Big Ideas Math Answers Grade 8 Chapter 2 Transformations provided helps students to learn the associated lessons easily. All the Solutions provided in BIM 8th Grade Chapter 2 Transformations are aligned according to the Transformation Textbook Chapter. Students can identify the knowledge gap accordingly and improvise on them and get a good hold of the &#8230; <a title=\"Big Ideas Math Answers Grade 8 Chapter 2 Transformations\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-8-chapter-2\/\" aria-label=\"More on Big Ideas Math Answers Grade 8 Chapter 2 Transformations\">Read more<\/a><\/p>\n","protected":false},"author":12,"featured_media":89220,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[4],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-2.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/32946"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/12"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=32946"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/32946\/revisions"}],"predecessor-version":[{"id":90357,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/32946\/revisions\/90357"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/89220"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=32946"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=32946"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=32946"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}