# Similarity Transformation Worksheet

Similarity Transformation Worksheet
• Page 1
1.
Find the scale factor of dilation of the triangle ABC to the triangle AED.

 a. 2 b. 2.5 c. 6.25 d. $\frac{1}{2}$

#### Solution:

Scale factor = AE / AB

= 20 / 8 = 5 / 2 = 2.5
[Substitute the values and simplify.]

So, the scale factor is 2.5.

2.
Find the scale factor of dilation of the rectangle ABCD to the rectangle AEFG.

 a. 5 b. $\frac{5}{3}$ c. 2.5 d. 3

#### Solution:

Scale factor = AB / AE

= 50 / 10 = 5
[Substitute the values and simplify.]

So, the scale factor is 5.

3.
Find the scale factor for the dilation.

 a. $\frac{3}{4}$ b. $\frac{3}{2}$ c. $\frac{4}{5}$ d. $\frac{2}{3}$

#### Solution:

Scale factor = New lengthOriginal length

= 22.50 / 15 = 1.5 = 3 / 2
[Substitute the values and simplify.]

So, the scale factor is 3 / 2.

4.
Find the scale factor for the dilation.

 a. 2.5 b. 6.5 c. 3 d. 2

#### Solution:

Scale factor = New lengthOriginal length

= 24 / 9.6 = 2.5
[Substitute the values and simplify.]

So, the scale factor is 2.5.

5.
Find the length of the base of the new triangle after reduction by a scale factor of $\frac{1}{4}$.

 a. 24 in. b. 12 in. c. 48 in. d. 3 in.

#### Solution:

Length of the base of the new triangle = Length of the base of the old triangle × scale factor

= 12 × 14 = 3
[Substitute the values and simplify.]

So, length of the base of the new triangle is 3 inches.

6.
A′B′C′D′ is a dilation of ABCD. Find the scale factor.

 a. 2 b. $\frac{1}{3}$ c. $\frac{3}{2}$ d. $\frac{2}{3}$

#### Solution:

To find the scale factor, we divide the length of one side of the dilated figure by the length of the corresponding side of the original figure.

= A'D'BC

= 128 = 3 / 2

7.
A parking lot is in the shape of a square measuring 19 ft by 12 ft. If you extend it by a scale factor of 3.5, find the new area of the parking lot.
 a. 2793 ft2 b. 228 ft2 c. 235 ft2 d. 798 ft2

#### Solution:

New area of the parking lot = Area of the original parking lot × (scale factor)2
[Increasing the length of a side of an object by factor x increases the area by factor x2 .]

= (19 × 12) × (3.5)2

= 2793 ft2

Therefore, the new area of the parking lot is 2793 ft2.

8.
Square ABCD is dilated by a scale factor of 2 with the center of dilation at (0, 0). What will be the area of the new square?

 a. It is 4 times the area of square ABCD. b. It is 2 times the area of square ABCD. c. It is $\frac{1}{4}$ the area of square ABCD. d. It is $\frac{1}{2}$ the area of square ABCD.

#### Solution:

New area of the square A′B′C′D′ = Area of the square ABCD × (scale factor)2
[Increasing the length of a side of an object by factor x increases the area by factor x2.]

= Area of the square ABCD × (2)2

= 4 × Area of the square ABCD

Therefore, the area of new square will be 4 times the area of square ABCD.

9.
A triangle of base 5 cm is enlarged to have a base of 8 cm. Find the scale factor.
 a. 5 b. $\frac{5}{8}$ c. 8 d. $\frac{8}{5}$

#### Solution:

Scale factor of a dilation describes the size of the change from the original figure to its image.

= 85

Therefore, the scale factor is 8 / 5.

10.
The length of a rectangle PQRS is 15 m. Find the measure of the dilation image for a scale factor of $\frac{4}{5}$.
 a. 12 m b. 15 m c. 7 m d. 18.75 m

#### Solution:

Length of the rectangle = 15 m

Scale factor = 4 / 5

Measure of the dilation image = length of the rectangle × scale factor

= 15 × 4 / 5 = 12 m

Therefore, the measure of the dilation image is 12 m.