1. A dilation is a transformation that changes the size of a figure but not its shape. The preimage and the image are always similar. A A’

2. Check It Out! Example 1
Tell whether each transformation appears to be a dilation. Explain. a. b.
Yes, the figures are similar and the image is not turned or flipped.
No, the figures are not similar.

3. A scale factor describes how much the figure is enlarged or reduced.
For a dilation with scale factor k, you can find the image of a point by multiplying each coordinate by k: (a, b)  (ka, kb).
k > 1 is an enlargement, or expansion.
0< k < 1 is a reduction, or contraction.

4. Example 1: Drawing and Describing Dilations
A. Apply the dilation D to the polygon with the given vertices. Describe the dilation.
D: (x, y) → (3x, 3y) A(1, 1), B(3, 1), C(3, 2)
A’ (3, 3), B’ (9, 3), C’ (9,6) scale factor 3

5. Example 1: Continued
B. Apply the dilation D to the polygon with the given vertices. Describe the dilation.
D: (x, y) →
P(–8, 4), Q(–4, 8), R(4, 4) 4 3 x, y
P’(-6, 3), Q’ (-3, 6), R’ (3, 3) scale factor 3/4

6. Check It Out! Example 1
Name the coordinates of the image points. Describe the dilation.
(x, y)→ ( ¼ x, ¼ y)
D(-8, 0), E(-8, -4), and F(-4, -8).
D'(-2, 0), E'(-2, -1), F'(-1, -2); scale factor 1/4