Identify and graph dilations LT 12.6

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. Example 1 Tell whether each transformation appears to be a dilation. Explain.

For a dilation with scale factor k, if k > 0, the figure is not turned or flipped. If k < 0, the figure is rotated by 180°. Helpful Hint 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.

Example 2 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.

Example 3 RSTU is transformed by a dilation centered at the origin. Identify the scale factor that produces an image with the following vertices: R’ (3, -3) U’ (1, 3) S’ (-10, 2) T’ (-1, 1) R S T U

Example 4