1. Objective
Identify and draw dilations.

2. Recall that a dilation is a transformation that changes the size of a figure but not the shape. The image and the preimage of a figure under a dilation are similar.

3. Example 1: Identifying Dilations
Tell whether each transformation appears to be a dilation. Explain. A. B.
No; the figures are not similar.
Yes; the figures are similar and the image is not turned or flipped.

4. Example 1a
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.

5. A dilation enlarges or reduces all dimensions proportionally
A dilation enlarges or reduces all dimensions proportionally. A dilation with a scale factor greater than 1 is an enlargement, or expansion. A dilation with a scale factor greater than 0 but less than 1 is a reduction, or contraction.

7. If the scale factor of a dilation is negative, the preimage is rotated by 180°. For k > 0, a dilation with a scale factor of –k is equivalent to the composition of a dilation with a scale factor of k that is rotated 180° about the center of dilation.

8. Example 2: Drawing Dilations in the Coordinate Plane
Draw the image of the triangle with vertices
P(–4, 4), Q(–2, –2), and R(4, 0) under a
dilation with a scale factor of centered at the origin.
The dilation of (x, y) is

9. Graph the preimage and image.
Example 2 Continued
Graph the preimage and image. P P’ Q’ R’ R Q