{"id":81736,"date":"2021-03-31T19:32:59","date_gmt":"2021-03-31T14:02:59","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=81736"},"modified":"2022-04-01T10:26:32","modified_gmt":"2022-04-01T04:56:32","slug":"eureka-math-grade-8-module-2-lesson-5","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/eureka-math-grade-8-module-2-lesson-5\/","title":{"rendered":"Eureka Math Grade 8 Module 2 Lesson 5 Answer Key"},"content":{"rendered":"

Engage NY Eureka Math 8th Grade Module 2 Lesson 5 Answer Key<\/h2>\n

Eureka Math Grade 8 Module 2 Lesson 5 Exercise Answer Key<\/h3>\n

Exercise 1.
\nLet there be a rotation of d degrees around center O. Let P be a point other than O. Select d so that d\u22650. Find P’ (i.e., the rotation of point P) using a transparency.
\n\"Eureka
\nAnswer:
\nVerify that students have rotated around center O in the counterclockwise direction.
\n\"Eureka<\/p>\n

Exercise 2.
\nLet there be a rotation of d degrees around center O. Let P be a point other than O. Select d so that d<0. Find P’ (i.e., the rotation of point P) using a transparency.
\n\"Eureka
\nAnswer:
\nVerify that students have rotated around center O in the clockwise direction.
\n\"Eureka<\/p>\n

Exercise 3.
\nWhich direction did the point P rotate when d\u22650?
\nAnswer:
\nIt rotated counterclockwise, or to the left of the original point.<\/p>\n

Exercise 4.
\nWhich direction did the point P rotate when d<0?
\nAnswer:
\nIt rotated clockwise, or to the right of the original point.<\/p>\n

Exercises 5\u20136<\/p>\n

Exercise 5.
\nLet L be a line, \\(\\overrightarrow{A B}\\) be a ray, \\(\\overline{\\boldsymbol{C D}}\\) be a segment, and \u2220EFG be an angle, as shown. Let there be a rotation of d degrees around point O. Find the images of all figures when d\u22650.
\n\"Eureka
\nAnswer:
\n\"Eureka
\nVerify that students have rotated around center O in the counterclockwise direction.<\/p>\n

Exercise 6.
\nLet \\(\\overline{A B}\\) be a segment of length 4 units and \u2220CDE be an angle of size 45\u00b0. Let there be a rotation by d degrees, where d<0, about O. Find the images of the given figures. Answer the questions that follow.
\n\"Eureka
\nAnswer:
\n\"Eureka
\nVerify that students have rotated around center O in the clockwise direction.<\/p>\n

a. What is the length of the rotated segment Rotation(AB)?
\nAnswer:
\nThe length of the rotated segment is 4 units.<\/p>\n

b. What is the degree of the rotated angle Rotation (\u2220CDE)?
\nAnswer:
\nThe degree of the rotated angle is 45\u00b0.<\/p>\n

Exercises 7\u20138<\/p>\n

Exercise 7.
\nLet L1<\/sub> and L2<\/sub> be parallel lines. Let there be a rotation by d degrees, where -360<d<360, about O.
\nIs (L1<\/sub> )’\u2225(L2<\/sub>)’?
\n\"Eureka
\nAnswer:
\n\"Eureka
\nVerify that students have rotated around center O in either direction. Students should respond that (L1<\/sub>)’ || (L2<\/sub>)’.<\/p>\n

Exercise 8.
\nLet L be a line and O be the center of rotation. Let there be a rotation by d degrees, where d\u2260180 about O. Are the lines L and L’ parallel?
\n\"Eureka
\nAnswer:
\n\"Eureka
\nVerify that students have rotated around center O in either direction any degree other than 180. Students should respond that L and L\u2019 are not parallel.<\/p>\n

Eureka Math Grade 8 Module 2 Lesson 5 Exit Ticket Answer Key<\/h3>\n

Question 1.
\nGiven the figure H, let there be a rotation by d degrees, where d\u22650, about O. Let Rotation(H) be H’.
\n\"Engage
\nAnswer:
\n\"Engage
\nSample rotation shown above. Verify that the figure H’ has been rotated counterclockwise with center O.<\/p>\n

Question 2.
\nUsing the drawing above, let Rotation1<\/sub> be the rotation d degrees with d<0, about O. Let Rotation_1 (H) be H”.
\nAnswer:
\nSample rotation shown above. Verify that the figure H” has been rotated clockwise with center O.<\/p>\n

Eureka Math Grade 8 Module 2 Lesson 5 Problem Set Answer Key<\/h3>\n

Question 1.
\nLet there be a rotation by -90\u00b0 around the center O.
\n\"Eureka
\nAnswer:
\nRotated figures are shown in red.
\n\"Eureka<\/p>\n

Question 2.
\nExplain why a rotation of 90 degrees around any point O never maps a line to a line parallel to itself.
\nAnswer:
\nA 90-degree rotation around point O will move a given line L to L’. Parallel lines never intersect, so it is obvious that a 90-degree rotation in either direction does not make lines L and L’ parallel. Additionally, we know that there exists just one line parallel to the given line L that goes through a point not on L. If we let P be a point not on L, the line L’ must go through it in order to be parallel to L. L’ does not go through point P; therefore, L and L’ are not parallel lines. Assume we rotate line L first and then place a point P on line L’ to get the desired effect (a line through P). This contradicts our definition of parallel (i.e., parallel lines never intersect); so, again, we know that line L is not parallel to L’.
\n\"Eureka<\/p>\n

Question 3.
\nA segment of length 94 cm has been rotated d degrees around a center O. What is the length of the rotated segment? How do you know?
\nAnswer:
\nThe rotated segment will be 94 cm in length. (Rotation 2) states that rotations preserve lengths of segments, so the length of the rotated segment will remain the same as the original.<\/p>\n

Question 4.
\nAn angle of size 124\u00b0 has been rotated d degrees around a center O. What is the size of the rotated angle? How do you know?
\nAnswer:
\nThe rotated angle will be 124\u00b0. (Rotation 3) states that rotations preserve the degrees of angles, so the rotated angle will be the same size as the original.<\/p>\n","protected":false},"excerpt":{"rendered":"

Engage NY Eureka Math 8th Grade Module 2 Lesson 5 Answer Key Eureka Math Grade 8 Module 2 Lesson 5 Exercise Answer Key Exercise 1. Let there be a rotation of d degrees around center O. Let P be a point other than O. Select d so that d\u22650. Find P’ (i.e., the rotation of … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[6],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/81736"}],"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\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=81736"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/81736\/revisions"}],"predecessor-version":[{"id":91806,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/81736\/revisions\/91806"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=81736"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=81736"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=81736"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}