7-1 Dilations

Apply the coordinate transformation for a dilation from the origin with a scale factor of 2.

• (0.5x, 0.5y)

• (2x, 2y)

• (x, y)

• (3x, 3y)

A rectangle is dilated with a scale factor of 3. If the original length of a side was 5 units, what is the new length?

• 20

• 15

• 8

• 10

Plot the points for the transformation D_1/3

What are the coordinates of D_{(2, X)} (△XYZ) for X(0, -8), Y(-3, -2), and Z(4.5, 0)?

Given that △A′B′C′ is a dilation of △ABC, how are the angles and side lengths of the preimage related to the angles and side lengths of the image?

• The angles are congruent and the side lengths are congruent.

• The angles are congruent and the side lengths are proportional.

• The angles are proportional and the side lengths are congruent.

• The angles are proportional and the side lengths are proportional.

What is the scale factor of the dilation shown?

• 3/2

• 3

• 2

• 2/3

What are the coordinates of R′ for the dilation D_{(0.5, P)}(▱PQRS)?

the x coordinate is​ (a)   and the y coordinate is​ (b)   .

The vertices of △JKL are J(−3, −2), K(1, 4), and L(4, 2). Which coordinate pairs are vertices of D₅(△JKL)?

• (−15, −10)

• (5, 20)

• (20, 10)

• (5, 4)

• (−15, −2)

A dilation maps △ABC to △A′B′C′. The area of △ABC is 13 square units, and the area of △A′B′C′ is 52 square units. What is the scale factor?

• 2

• 4

• 13

• 26

Answer explanation

Remember that area is in units² so you are multiplying two lengths together. If the ratio of their areas is 4/1, then it means the ratio of their lengths must be 2/1. (i.e. 2/1 * 2/1 = 4/1)