1. DILATIONS Content Standards G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). G.SRT.1 Understand similarity in terms of similarity transformations. Verify experimentally the properties of dilations given by a center and a scale factor: a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. Mathematical Practices 1 Make sense of problems and persevere in solving them. 5 Use appropriate tools strategically.

2. Concept

3. Example 1 Draw a Dilation Copy trapezoid PQRS and point C. Then use a ruler to draw the image of trapezoid PQRS under a dilation with center C and scale factor 3. Since k > 1, the dilation is an enlargement of trapezoid PQRS.

4. Example 1 Draw a Dilation Locate P', Q', R', and S' so that Copy trapezoid PQRS and point C. Then use a ruler to draw the image of trapezoid PQRS under a dilation with center C and scale factor 3.

5. Example 1 Draw a Dilation Answer: Draw trapezoid P'Q'R'S'. Copy trapezoid PQRS and point C. Then use a ruler to draw the image of trapezoid PQRS under a dilation with center C and scale factor 3.

6. Concept

7. Example 3 Dilations in the Coordinate Plane Trapezoid EFGH has vertices E(–8, 4), F(–4, 8), G(8, 4) and H(–4, –8). Graph the image of EFGH after a dilation centered at the origin with a scale factor of Multiply the x- and y-coordinates of each vertex by the scale factor,

8. Example 3 Dilations in the Coordinate Plane Graph the preimage and image. Answer: E'(–2, 1), F'(–1, 2), G'(2, 1), H'(–1, –2)