Topics
3. Geometry
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United States of AmericaFL
Grade 8

3.08 Dilations

Lesson
Worksheet
Practice
Worksheet
Dilations
1

Determine whether each statement is true or false and justify your answer:

a

Any dilation with a scale factor less than 1 is a reduction.

b

Any dilation with a scale factor greater than 1 is an enlargement.

2

Determine whether the following graphs show a dilation. If yes, find the scale factor.

a
2
4
6
8
10
12
14
16
18
x
2
4
6
8
10
12
14
16
18
y
b
2
4
6
8
10
12
14
16
18
x
2
4
6
8
10
12
14
16
18
y
c
-8
-6
-4
-2
2
4
6
8
x
-8
-6
-4
-2
2
4
6
8
y
d
-8
-6
-4
-2
2
4
6
8
x
-8
-6
-4
-2
2
4
6
8
y
3

Find the scale factor for each pair of similar figures:

a
b
c
d
4

Dilate the figure by the given factor using the origin as the center of dilation:

a

Scale factor of 4

2
4
6
8
10
12
14
16
18
20
x
2
4
6
8
10
12
14
16
18
20
y
b

Scale factor of 3

2
4
6
8
10
12
14
16
x
2
4
6
8
10
12
14
16
y
c

Scale factor of 2

2
4
6
8
10
12
14
16
18
x
2
4
6
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10
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14
16
18
y
d

Scale factor of 4

2
4
6
8
10
12
14
16
18
20
x
2
4
6
8
10
12
14
16
18
20
y
e

Scale factor of \dfrac{1}{2}

2
4
6
8
10
12
14
16
18
x
2
4
6
8
10
12
14
16
18
y
f

Scale factor of \dfrac{1}{2}

-6
-4
-2
2
4
6
8
10
x
-6
-4
-2
2
4
6
8
10
y
g

Scale factor of \dfrac{1}{2}

-8
-6
-4
-2
2
4
6
8
x
-8
-6
-4
-2
2
4
6
8
y
h

Scale factor of \dfrac{5}{4}

2
4
6
8
10
12
14
16
18
20
x
2
4
6
8
10
12
14
16
18
20
y
5

Dilate each figure using the given scale factor and center of dilation:

a

Scale factor: 2

Center of dilation: A\left(2, 3\right)

2
4
6
8
10
12
14
16
18
x
2
4
6
8
10
12
14
16
18
y
b

Scale factor: 2

Center of dilation: A\left(1, 2\right)

2
4
6
8
10
12
14
16
18
20
22
24
x
2
4
6
8
10
12
14
16
18
20
22
24
y
c

Scale factor: \dfrac{1}{2}

Center of dilation: A\left(3, 2\right)

2
4
6
8
10
12
14
16
18
x
2
4
6
8
10
12
14
16
18
y
d

Scale factor: \dfrac{1}{5}

Center of dilation: A\left(1, 1\right)

2
4
6
8
10
12
14
16
18
x
2
4
6
8
10
12
14
16
18
y
6

A triangle with vertices A\left( - 7 , - 5 \right), B\left(3, - 5 \right) and C\left( - 5 , 9\right) is dilated by a factor of 0.5 using the origin as the center of dilation. What are the coordinates of the vertices of the dilated triangle?

7

A rectangle with vertices P\left( - 5 , 3\right), Q\left(3, 3\right), R\left(3, - 5 \right), and R\left( - 5 , - 5 \right) is dilated using the origin as the center of dilation. The vertices of the new rectangle are P'\left( - 25 , 15\right), Q'\left(15, 15\right), R'\left(15, - 25 \right), and S'\left( - 25 , - 25 \right).

Find the scale factor.

8

If a square with a perimeter of 20 \text{ in} is dilated by a factor of 0.6, find the side length of the dilated square.

9

If a square with an area of 25 \text{ ft}^{2} is dilated by a factor of 0.4, find the side length of the dilated square.

10

\triangle ABC is dilated by a scale factor with a center of dilation at the origin to obtain triangle A'B'C':

Find the scale factor.

1
2
3
4
5
6
7
8
9
x
1
2
3
4
5
6
7
8
9
y
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Outcomes

MA.8.GR.2.2

Given a preimage and image generated by a single dilation, identify the scale factor that describes the relationship.

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