Dilation Worksheet

**Page 1**

1.

Which of the following is/are correct?

1. Every dilation has a center.

2. Every dilation has a scale factor.

3. Every dilation increases the size of the picture.

4. Every dilation is a transformation.

1. Every dilation has a center.

2. Every dilation has a scale factor.

3. Every dilation increases the size of the picture.

4. Every dilation is a transformation.

a. | 2, 3, and 4 only | ||

b. | 1, 2 and 4 only | ||

c. | 1, 2 and 3 only | ||

d. | All are correct |

Every dilation is a transformation.

A dilation can either increase or decrease the size of the original picture.

Statements 1, 2 and 4 only are correct.

Correct answer : (2)

2.

Select the correct statement/ statements.

1. P is the center of dilation

2. Scale factor of the dilation $x$ maps Q′ to Q

3. QQ′ = PQ ($x$ - 1)

1. P is the center of dilation

2. Scale factor of the dilation $x$ maps Q′ to Q

3. QQ′ = PQ ($x$ - 1)

a. | All are correct | ||

b. | 2 and 3 only | ||

c. | 1 and 3 only | ||

d. | 1 and 2 only |

Scale factor of

QQ′ = PQ′ - PQ =

Statements 1 and 3 only are correct.

Correct answer : (3)

3.

What is the scale factor that maps square ABCD to square AEFG?

[Given $a$ = 2 and $b$ = 10.]

[Given $a$ = 2 and $b$ = 10.]

a. | 6 | ||

b. | 12 | ||

c. | 5 | ||

d. | $\frac{1}{5}$ |

=

=

Correct answer : (1)

4.

Find the scale factor that maps PQRS onto ABCD.

a. | 1.5 | ||

b. | 3 | ||

c. | 2 | ||

d. | 0.5 |

=

= 0.5

Correct answer : (4)

5.

Find the image of point $P$ (3, 4) under dilation with center (0, 0) with a scale factor of 2.

a. | (- 3, - 4) | ||

b. | (6, 8) | ||

c. | (- 6, 8) | ||

d. | (6, - 8) |

Image of

= (6, 8)

Correct answer : (2)

6.

Find the image of M(- 6, 12) under dilation with center as origin and with a scale factor of $\frac{5}{6}$.

a. | (- 5, 10) | ||

b. | (- 7, 14) | ||

c. | (5 , - 10) | ||

d. | (7, - 14) |

Image of M(- 6, 12) = (- 6 ×

= (- 5, 10)

Correct answer : (1)

7.

Find the point of the image of point A after a dilation with center at the origin and scale factor of 2.5.

a. | R | ||

b. | P | ||

c. | Q | ||

d. | M |

When it is under dilation with a scale factor of 2.5, the image will be (- 4 × 2.5, 2 × 2.5) = (- 10, 5).

This point is shown as P in the picture.

Correct answer : (2)

8.

Find the scale factor when Q is dilated to P with center O.

a. | 4 | ||

b. | $\frac{1}{4}$ | ||

c. | 3 | ||

d. | $\frac{1}{3}$ |

P is (4, - 3).

The coordinates of P are

Scale factor is

Correct answer : (4)

9.

Select the dilated image of ABCD under a scale factor of 3.

a. | Neither figure 1 nor figure 2 | ||

b. | Figure 1 | ||

c. | Figure 2 | ||

d. | Both Figure 1 and Figure 2 |

But Figure 1, is not of the same shape of the original. Point C′ is not shown as dilated under a scale facor of 3. So, it is not a transformation.

Figure 2 is of similar size of that of the original. All the points are dilated under a scale factor of 3. It is a transformation.

Figure 2 is the dilation of ABCD under a scale factor of 3.

Correct answer : (3)

10.

Points A(1, 1) and B(9, 6) on an XY plane are dilated to A′ and B′ with the center as the origin. The scale factor of A is 4 and that of B is $\frac{1}{3}$. Find the difference in the lengths between the line segments AB and A′ B′.

a. | $\sqrt{63}-\sqrt{13}$ units | ||

b. | 3$\sqrt{4}$ units | ||

c. | $\sqrt{89}-\sqrt{5}$ units | ||

d. | $\frac{4}{3}$units |

[Given.]

A′ = (4, 4)

[Multiply the coordinates by the scale factor.]

B′ = (3, 2)

[Multiply the coordinates by the scale factor.]

AB =

[Distance formula.]

=

[Simplify.]

A′B′ =

[Distance formula.]

A′B′ =

[Simplify.]

AB - A′B′ =

[Steps 5 and 7.]

Correct answer : (3)