Dilations Answers

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Carly stated, “All pairs of rectangles are dilations.” Which pair of rectangles would prove that Carly’s statement is incorrect?

A
A rectangle with length 4 and width 2. A rectangle with length 8 and width 4.
Option A
B
A rectangle with length 4 and width 2. A rectangle with length 6 and width 3.
Option B
C
A rectangle with length 4 and width 3. A rectangle with length 3 and width 2.
Option C
D
A rectangle with length 4 and width 3. A rectangle with length 2 and width 1.5.
Option D
3

Which statement about these rectangles is true?

Question illustration
A
The dilation is an enlargement.
B
The dilation is a reduction.
C
It is not a dilation.
D
There is not enough information.
4

The square shown is dilated by a scale factor of 2. The center of dilation is point C. Which shows the correct image, A’ ?

Question illustration
A
Point C is inside of square A. Square A prime is double the size of square A prime.
Option A
B
Point C is inside of square A. Square A prime is half the size of square A prime.
Option B
C
Point C is inside of square A. Square A prime is half the size of square A prime.
Option C
D
Point C is inside of square A. Square A prime is half the size of square A prime.
Option D
5

Joseph is creating a dilation through point B with a scale factor of 2. Which statements about the dilation are correct? Check all that apply.

Question illustration
A
A’ will be located on ray .
Option A
B
B and B’ are the same point.
C
will be as long as .
Option C
D
and will be part of the image’s sides.
Option D
E
The image will be inside the pre-image.
6

Elijah was trying to determine whether one triangle is a dilation of the other. Which statements about his solution are true? Check all that apply.Elijah’s work: 3 is not a factor of 5, so it must be a relationship with addition. Therefore, the triangles are not proportional and cannot form a dilation.

Question illustration
A
Elijah did not know that scale factors can be fractions or decimals greater than zero.
B
Elijah did not know that dilations are proportional and the relationships are multiplicative, not additive.
C
Elijah should have compared the ratios to determine if they are equivalent.
Option C
D
Elijah needs to know which triangle is the pre-image and which triangle is the image in order to determine if they are proportional.
E
Elijah needs labels on the points to determine which sides correspond when writing the ratios.
8

Which statement about a dilation with a scale factor of 3 is true?

A
Three is added to each side in the pre-image to find the corresponding side length in the image.
B
Three is subtracted from each side in the pre-image to find the corresponding side length in the image.
C
Each side in the pre-image is multiplied by three to find the corresponding side length in the image.
D
Each side in the pre-image is divided by three to find the corresponding side length in the image.
9

Which proportion could be used to determine if the figures represent a dilation?

Question illustration
A
Three-halves = StartFraction 6 Over 4 EndFraction
Option A
B
Three-halves = StartFraction 4 Over 6 EndFraction
Option B
C
Three-fourths = StartFraction 6 Over 2 EndFraction
Option C
D
Three-fourths = StartFraction 2 Over 6 EndFraction
Option D

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Dilations Answers — SRC 2022 MJ Grade 8…