Eureka Math Grade 8 Module 3 Mid Module Assessment Answer Key

Engage NY Eureka Math 8th Grade Module 3 Mid Module Assessment Answer Key

Eureka Math Grade 8 Module 3 Mid Module Assessment Task Answer Key

Question 1.
Use the figure below to complete parts (a) and (b).
Eureka Math Grade 8 Module 3 Mid Module Assessment Task Answer Key 1

Answer:
Eureka Math Grade 8 Module 3 Mid Module Assessment Task Answer Key 1.1

a. Use a compass and ruler to produce an image of the figure with center O and scale factor r=2.

b. Use a ruler to produce an image of the figure with center O and scale factor r=\(\frac{1}{2}\).

Question 2.
Use the diagram below to answer the questions that follow.

Let D be the dilation with center O and scale factor r>0 so that Dilation(P)=P’ and Dilation(Q)=Q’.
Eureka Math Grade 8 Module 3 Mid Module Assessment Task Answer Key 2
a. Use lengths |OQ|=10 units and |OQ’ |=15 units to determine the scale factor r of dilation D. Describe how to determine the coordinates of P’ using the coordinates of P.
Answer:
|OQ|r= |OQ’|
Eureka Math Grade 8 Module 3 Mid Module Assessment Task Answer Key 500
r = \(\frac{15}{10}\)
r = \(\frac{3}{2}\)
The same factor is r = \(\frac{3}{2}\)
Since the coordinates of P = (-4, -3) the coordinates of the dilated point P’ will be the same factor times the coordinates of P. Therefore P’ = (\(\frac{3}{2}\) × (-4), \(\frac{3}{2}\) × (-3)) = (-6, -45)

b. If |OQ|=10 units, |OQ’|=15 units, and |P’Q’|=11.2 units, determine |PQ|. Round your answer to the tenths place, if necessary.
Answer:
\(\frac{15}{10}\) = \(\frac{11.2}{|PQ|}\)
15(|PQ|) = 112
|PQ| = \(\frac{112}{15}\) ≈ 7.5
The length of \(\overline{P Q}\) is about 7.5 units.

Question 3.
Use a ruler and compass, as needed, to answer parts (a) and (b).

a. Is there a dilation D with center O that would map figure PQRS to figure P’Q’R’S’? Explain in terms of scale factor, center, and coordinates of corresponding points.
Eureka Math Grade 8 Module 3 Mid Module Assessment Task Answer Key 3
Answer:
Eureka Math Grade 8 Module 3 Mid Module Assessment Task Answer Key 3.1
P = (3, -2)
P’ = (9, -6)
Q = (3, -1)
Q’ = (9, -3)
R = (4, 1)
R’ = (12, 3)
S = (0, 2)
S’ = (0, 6)
Yes, there is a dilation D with Genter O, that maps PQS to P’Q’R’S’. The scale factor is 3. The image of each point is 3 times the coordinates of the original image. For example, P = (3, -2) and P’ = (3 × 3, 3 × (-2)) = (9, -6)

b. Is there a dilation D with center O that would map figure PQRS to figure P’Q’R’S’? Explain in terms of scale factor, center, and coordinates of corresponding points.
Eureka Math Grade 8 Module 3 Mid Module Assessment Task Answer Key 4
Answer:
Eureka Math Grade 8 Module 3 Mid Module Assessment Task Answer Key 4.1
No, there is not a dilation D that will map PQRS to P’Q’R’S’. A dilation will move A point, S, to its image S’ on the ray \(\overrightarrow{O S}\). In the picture above O, S, S’ are not on the same ray. A similar statement can be made for points P, Q and R, Therefore, there is no dilation that maps PQRS to P’Q’R’S’.

c. Triangle ABC is located at points A(-4,3), B(3,3), and C(2,-1) and has been dilated from the origin by a scale factor of 3. Draw and label the vertices of triangle ABC. Determine the coordinates of the dilated triangle A’B’C’, and draw and label it on the coordinate plane.
Eureka Math Grade 8 Module 3 Mid Module Assessment Task Answer Key 5
Answer:
Eureka Math Grade 8 Module 3 Mid Module Assessment Task Answer Key 5.1
A= (-4, 3)
A’ = (-4×3, 3×3) = (-12, 9)
B =(3, 3)
B’ = (3×3, 3×3) = (9, 9)
C = (2, -1)
C’ = (2×3, -1×3) = (6, -3)

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