1. Lesson 9.6 - Dilations Standard G.2.4

2. What is a Dilation? A Dilation is when an entire graph is enlarged or shrunk by a scale factor. Unlike reflections, translations, and rotations, a congruent figure is not produced. A Dilation is when an entire graph is enlarged or shrunk by a scale factor. Unlike reflections, translations, and rotations, a congruent figure is not produced.

3. Scale Factors The scale factor of a dilation is the amount that the graph is enlarged or shrunk by. The scale factor of a dilation is the amount that the graph is enlarged or shrunk by. If the scale factor is larger than 1, then the graph is enlarged. If the scale factor is smaller than 1, then the graph is shrunk.

4. Example Dilate ΔABC around the origin where A(1, 3), B(0, -1), and C(2, -3) by a scale factor of 2. Dilate ΔABC around the origin where A(1, 3), B(0, -1), and C(2, -3) by a scale factor of 2. A B C To Dilate, multiply all of the x and y values by the given scale factor. A’(2, 6), B’(0, -2), C’(4, -6) A’ B’ C’

5. You Try This One… Dilate ΔDEF around the origin where D(6, 0), E(-3, -2), F(-6, 4) if the scale factor is 1 / 3 Dilate ΔDEF around the origin where D(6, 0), E(-3, -2), F(-6, 4) if the scale factor is 1 / 3 D E F Divide all of the x and y values by 3 D’(2, 0), E’(-1, - 2 / 3 ) and F’(-2, 4 / 3 ) D’ E’ F’

6. A Final Example The pre-image in this picture is yellow and the image is red. Was the image enlarged or shrunk? By what scale factor? The pre-image in this picture is yellow and the image is red. Was the image enlarged or shrunk? By what scale factor? Shrunk with a scale factor of 1 / 3 (0, -2) (0, -6)

7. Homework Worksheet 9.6 Worksheet 9.6