EXAMPLE 1 Identify dilations

Find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement.

a.

SOLUTION

a. Because = , the scale factor is k = .

The image P’ is an enlargement.

CP’CP

128

32

EXAMPLE 1 Identify dilations

Find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement.

b.

SOLUTION

Because = , the scale factor is k = .

The image P’ is a reduction.

CP’CP

1830’

35

b.

EXAMPLE 2 Draw a dilation

Draw and label DEFG. Then construct a dilation of DEFG with point D as the center of dilation and a scale factor of 2.

SOLUTION

STEP 1

Draw DEFG. Draw rays from D through vertices E, F, and G.

EXAMPLE 2 Draw a dilation

STEP 2

Open the compass to the length of DE . Locate E’ on DE so DE’ = 2(DE). Locate F’ and G’ the same way.

EXAMPLE 2 Draw a dilation

STEP 3

Add a second label D’ to point D. Draw the sides of D’E’F’G’.

GUIDED PRACTICE for Examples 1 and 2

1. In a dilation, CP’ = 3 and CP = 12. Tell whether the dilation is a reduction or an enlargement and find its scale factor.

Because = , the scale factor is k = .

The image P’ is a reduction.

CP’CP

312

14

ANSWER

GUIDED PRACTICE for Examples 1 and 2

2. Draw and label RST. Then construct a dilation of RST with R as the center of dilation and a scale factor of 3.

ANSWER