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. | $\frac{1}{2}$ |

=

[Substitute the values and simplify.]

So, the scale factor is 2.5.

Correct answer : (2)

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 |

=

[Substitute the values and simplify.]

So, the scale factor is 5.

Correct answer : (1)

3.

Find the scale factor for the dilation.

a. | $\frac{3}{4}$ | ||

b. | $\frac{3}{2}$ | ||

c. | $\frac{4}{5}$ | ||

d. | $\frac{2}{3}$ |

=

[Substitute the values and simplify.]

So, the scale factor is

Correct answer : (2)

4.

Find the scale factor for the dilation.

a. | 2.5 | ||

b. | 6.5 | ||

c. | 3 | ||

d. | 2 |

=

[Substitute the values and simplify.]

So, the scale factor is 2.5.

Correct answer : (1)

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. |

= 12 ×

[Substitute the values and simplify.]

Correct answer : (4)

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. | $\frac{2}{3}$ |

Scale factor =

=

[AD = BC.]

=

Correct answer : (3)

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 ft ^{2} | ||

b. | 228 ft ^{2} | ||

c. | 235 ft ^{2} | ||

d. | 798 ft ^{2} |

[Increasing the length of a side of an object by factor

= (19 × 12) × (3.5)

= 2793 ft

Therefore, the new area of the parking lot is 2793 ft

Correct answer : (1)

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. |

[Increasing the length of a side of an object by factor

= Area of the square ABCD × (2)

= 4 × Area of the square ABCD

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

Correct answer : (1)

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. | $\frac{8}{5}$ |

=

Therefore, the scale factor is

Correct answer : (4)

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 |

Scale factor =

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

= 15 ×

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

Correct answer : (1)