## 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.

Answer:

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?

Answer:

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: (_____, _____)

Answer:

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.

Answer:

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?

Answer:

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?

Answer:

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: (_____, _____)

Answer:

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)