Lesson 1: Dilations Answers

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Dilation was performed on a rectangle. How does the image relate to the pre-image? Select three options.The image is a reduction because 0 < n < 1.The side lengths of the image are two-fifths the size of the corresponding side lengths of the pre-image.The angles of the image are two-fifths the size of the angles of the pre-image.The center of dilation is at point Q.The base of the image is two-fifths the size of the base of the pre-image.

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A
The image is a reduction because 0 < n < 1.
B
The side lengths of the image are two-fifths the size of the corresponding side lengths of the pre-image.
C
The angles of the image are two-fifths the size of the angles of the pre-image.
D
The center of dilation is at point Q.
E
The base of the image is two-fifths the size of the base of the pre-image.
2
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Which statements justify that the dilation of triangle STU is an enlargement increasing its size by the magnitude of the scale factor? Select two options.

A
The triangle pre-image is closer to the point of dilation than the image.
B
The triangle image is closer to the point of dilation than the pre-image.
C
The value of the scale factor, , is between 0 and 1.
Option C
D
The value of the scale factor, 6, is greater than 1.
E
The vertices of the pre-image are collinear with the vertices of the image.
3

Line segment AB is dilated to create line segment A'B' using point Q as the center of dilation.

Question illustration
A
1
B
1.25
C
2
D
2.5
4

Point C is the center of dilation. Line segment B A is dilated to create line segment B prime A prime. The length of C A is 4. The length of A A prime is 16.

Question illustration
A
One-fifth
Option A
B
One-fourth
Option B
C
4
D
5
5

The perimeter of ΔABC is 13 cm. It was dilated to create ΔA'B'C'.

Question illustration
A
13 cm
B
26 cm
C
39 cm
D
52 cm
6

Triangle TUV was dilated to create triangle T'U'V' using point A as the center of dilation.

Question illustration
A
Two-fifths
Option A
B
Two-thirds
Option B
C
Three-halves
Option C
D
Eight-fifths
Option D
7

Line segment XY is dilated to create line segment X'Y' using point T as the center of dilation.

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A
3 units
B
6 units
C
12 units
D
15 units
8

Triangle JKL was dilated using the rule . The image, triangle J'K'L', is the result of the dilation.

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A
5 units
B
7.5 units
C
10 units
D
12.5 units
9

Rectangle WXYZ was dilated to create W'X'Y'Z'.

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A
0.5 units
B
1.2 units
C
1.5 units
D
1.8 units
10

Triangle ABC was dilated using the rule DO,4. Triangle A'B'C' is the result of the dilation.

Question illustration
A
1.5 units
B
3 units
C
4.5 units
D
6 units

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