9.5 Dilations

Dilations: A transformation that produces an image that is the same shape as the original (pre-image), but is a different size. Pre-Image and image(΄) are not congruent-THEY ARE SIMILAR! Every description should include a scale factor and center of dilation Reduction if 0<scale factor (n)<1 Enlargement if scale factor (n)>1 To find the scale factor (n), compare, as a ratio, the length on the image to the length on the preimage.

Identifying Dilations: finding scale factor Center: C P P´ 6 5 P´ P 3 2 Q´ Q • • R C C R´ Q R´ Q´ R Reduction: n = = = 3 6 1 2 CP CP Enlargement: n = = 5 2 CP CP

Identifying Dilations Identify the dilation and find its scale factor. • C P P´ 2 3

Checkpoint? Identify the dilation and find its scale factor. • P´ 2 P 1 2

Coordinate Plane Dilations: Identify the dilation and find its scale factor.

Checkpoint? Identify the dilation and find its scale factor.

Dilations in the Coordinate Plane In a coordinate plane, dilations whose centers are the origin have the property that the image of P(x, y) is P´(nx, ny). Draw a dilation of rectangle ABCD with A(2, 2), B(6, 2), C(6, 4), and D(2, 4). Use the origin as the center and use a scale factor of . How does the perimeter of the preimage compare to the perimeter of the image? 1 2 y D C D´ A C´ B A(2, 2)  A´(1, 1) A´ B(6, 2)  B´(3, 1) 1 B´ • C(6, 4)  C ´(3, 2) O 1 x D(2, 4)  D´(1, 2)

Using Dilations in Real Life Shadow puppets have been used in many countries for hundreds of years. A flat figure is held between a light and a screen. The audience on the other side of the screen sees the puppet’s shadow. The shadow is a dilation, or enlargement, of the shadow puppet. When looking at a cross sectional view, LCP ~ LSH. The shadow puppet shown is 12 inches tall (CP in the diagram). Find the height of the shadow, SH, for the distance from the screen. In each case, by what percent is the shadow larger than the puppet? LC = LP = 59 in.; LS = LH = 74 in.

9.5 Homework Workbook p. 239-240 #2-20 even