## Engage NY Eureka Math 5th Grade Module 6 Lesson 16 Answer Key

### Eureka Math Grade 5 Module 6 Lesson 16 Problem Set Answer Key

Question 1.
Use the coordinate plane below to complete the following tasks.

a. Draw $$\overline{A B}$$.
b. Plot point C (0, 8).
c. Draw $$\overline{A C}$$.
d. Explain how you know ∠CAB is a right angle without measuring it.
e. Sean drew the picture below to find a segment perpendicular to (AB) ̅. Explain why Sean is correct.

d.
Explanation :
∠CAB is a right angle because I can Draw a triangle that has $$\overline{A B}$$ has its long side. The length is 5 units and the Height is 2 units . When I slide the triangle to the left and rotated, I know 2 acute angles will form a 90 degrees or right angle .
e.
Sean is correct because I notice that he slid and rotated the triangle and the 2 acute angles form the right angle .

Question 2.
Use the coordinate plane below to complete the following tasks.

a. Draw $$\overline{Q T}$$.
b. Plot point R (2, 6$$\frac{1}{2}$$).
c. Draw $$\overline{Q R}$$.
d. Explain how you know ∠RQT is a right angle without measuring it.
e. Compare the coordinates of points Q and T. What is the difference of the x-coordinates? The y-coordinates?
f. Compare the coordinates of points Q and R. What is the difference of the x-coordinates? The y-coordinates?
g. What is the relationship of the differences you found in parts (e) and (f) to the triangles of which these two segments are a part?

d.
Explanation :
Triangles are drawn when I slid and rotated the triangle. I know that 2 acute angles will form 90 degrees. If they form 90 degrees the angle between them , ∠RQT will be 90 degrees Since the 3 angles form a straight line .
e. The coordinates of points Q and T are ( 3$$\frac{1}{2}$$ , 4 ) and (6, 5$$\frac{1}{2}$$) Respectively .
The differences of x- coordinate = 6 – 3$$\frac{1}{2}$$= 2$$\frac{1}{2}$$ .
The difference of y-coordinate = 5$$\frac{1}{2}$$ – 4 = 1$$\frac{1}{2}$$.
f. The coordinates of points Q and R are ( 3$$\frac{1}{2}$$ , 4 ) and (2, 6$$\frac{1}{2}$$) Respectively .
The differences of x- coordinate = 3$$\frac{1}{2}$$ – 2 = 1$$\frac{1}{2}$$ .
The difference of y-coordinate = 6$$\frac{1}{2}$$ – 4 = 2$$\frac{1}{2}$$.
g. The differences in the X-coordinate of the points Q and T is same as the differences in the Y-coordinate of the points Q and R .
The differences in the Y-coordinate of the points Q and T is same as the differences in the X-coordinate of the points Q and R. Just        the Numbers flipped.

Question 3.
$$\overline{E F}$$ contains the following points. E: (4, 1) F: (8, 7)
Give the coordinates of a pair of points G and H, such that $$\overline{E F}$$ ⊥ $$\overline{G H}$$.
G: (_____, _____) H: (_____, _____)
As the above rule is applied of Question -2-g and the Coordinate of Points are written .
G: (1, 8) H: ( 7, 4)

### Eureka Math Grade 5 Module 6 Lesson 16 Exit Ticket Answer Key

Use the coordinate plane below to complete the following tasks.
a. Draw $$\overline{U V}$$.
b. Plot point W (4$$\frac{1}{2}$$,6).
c. Draw $$\overline{V W}$$.
d. Explain how you know that ∠UVW is a right angle without measuring it.

d.
Explanation :
Triangles are drawn when I slid and rotated the triangle. I know that 2 acute angles will form 90 degrees. If they form 90 degrees the angle between them , ∠UVW will be 90 degrees Since the 3 angles form a straight line .

### Eureka Math Grade 5 Module 6 Lesson 16 Homework Answer Key

Question 1.
Use the coordinate plane below to complete the following tasks.

a. Draw $$\overline{P Q}$$.
b. Plot point R (3, 8).
c. Draw $$\overline{P R}$$.
d. Explain how you know ∠RPQ is a right angle without measuring it.
e. Compare the coordinates of points P and Q. What is the difference of the x-coordinates? The y-coordinates?
f. Compare the coordinates of points P and R. What is the difference of the x-coordinates? The y-coordinates?
g. What is the relationship of the differences you found in parts (e) and (f) to the triangles of which these two segments are a part?

d. Explanation :
Triangles are drawn when I slid and rotated the triangle. I know that 2 acute angles will form 90 degrees. If they form 90 degrees the angle between them , ∠RPQ will be 90 degrees Since the 3 angles form a straight line .
e. The coordinates of points P and Q are ( 2, 4 ) and (6, 3) Respectively .
The differences of x- coordinate = 6 – 2= 4 .
The difference of y-coordinate = 4- 3 = 1.
f. The coordinates of points P and R are ( 2, 4 ) and ( 3, 8 ) Respectively .
The differences of x- coordinate = 3 – 2 = 1
The difference of y-coordinate = 8 – 4 = 4
g. The differences in the X-coordinate of the points P and Q  is same as the differences in the Y-coordinate of the points P and R .
The differences in the Y-coordinate of the points P and Q is same as the differences in the X-coordinate of the points P and R . Just        the Numbers flipped.

Question 2.
Use the coordinate plane below to complete the following tasks.

a. Draw $$\overline{C B}$$.
b. Plot point D($$\frac{1}{2}$$, 5$$\frac{1}{2}$$).
c. Draw $$\overline{C D}$$.
d. Explain how you know ∠DCB is a right angle without measuring it.
e. Compare the coordinates of points C and B. What is the difference of the x-coordinates? The y-coordinates?
f. Compare the coordinates of points C and D. What is the difference of the x-coordinates? The y-coordinates?
g. What is the relationship of the differences you found in parts (e) and (f) to the triangles of which these two segments are a part?

d. Explanation :
Triangles are drawn when I slid and rotated the triangle. I know that 2 acute angles will form 90 degrees. If they form 90 degrees the angle between them , ∠DCB will be 90 degrees Since the 3 angles form a straight line .
e. The coordinates of points C and B. are (1$$\frac{3}{4}$$, 4 ) and (3$$\frac{1}{4}$$, 5) Respectively .
The differences of x- coordinate = 3$$\frac{1}{4}$$ – 1$$\frac{3}{4}$$ = $$\frac{13}{4}$$ –$$\frac{7}{4}$$ = 1$$\frac{6}{4}$$=$$\frac{2}{3}$$
The difference of y-coordinate = 5 – 4 =1
f. The coordinates of points C and D are (1$$\frac{3}{4}$$, 4 ) and ($$\frac{1}{2}$$, 5$$\frac{1}{2}$$) Respectively .
The differences of x- coordinate = 1$$\frac{3}{4}$$ – $$\frac{1}{2}$$ = $$\frac{7}{4}$$– $$\frac{2}{4}$$= $$\frac{5}{4}$$= 1$$\frac{1}{4}$$
The difference of y-coordinate =5$$\frac{1}{2}$$ – 4 = 1$$\frac{1}{2}$$
g. All the differences are different .No Relationship is formed .

Question 3.
$$\overline{S T}$$ contains the following points. S: (2, 3) T: (9, 6)
Give the coordinates of a pair of points, U and V, such that $$\overline{S T}$$ ⊥ $$\overline{S T}$$.
U: (_____, _____) V: (_____, _____)

the coordinates of a pair of points, U and V, such that $$\overline{S T}$$ ⊥ $$\overline{S T}$$.
U: (, ) V: (_____, _____)
The coordinates of points S and T are(2, 3) and (9, 6) Respectively .
The differences of x- coordinate = 9 – 2= 7 .
The difference of y-coordinate = 6- 3 = 3.

The coordinates of points T and (6, 13) are (9, 6) and (6, 13)
The differences of x- coordinate = 9 – 6 = 3
The difference of y-coordinate = 13 – 6 = 7

The differences in the X-coordinate of the points S and T  is same as the differences in the Y-coordinate of the points T and (6, 13) .
The differences in the Y-coordinate of the points S and T is same as the differences in the X-coordinate of the points T and (6, 13) .        Just the Numbers flipped.
U: (3, 9) V: (6, 2)