12-7 Dilations.

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Presentation transcript:

12-7 Dilations

Transformations The transformations we have studied thus far have all been isometries. Reflection Translation Glide Reflection Rotation

Dilations The last transformation that we will study is the dilation.

Dilations A dilation is a transformation whose preimage and image are similar. Remember, an isometry is a transformation in which the preimage and image are congruent. Therefore, a dilation is not, in general, an isometry.

Dilations Every dilation has a center and a scale factor n, where n must be > 0. The scale factor describes the size change from the original figure to its image.

Enlargements A dilation is an enlargement if the scale factor is greater than 1. 6 Enlargement Center C Scale Factor 3 2 C

Reductions A dilation is a reduction if the scale factor is between 0 and 1. E D B A 8 Reduction Center C Scale Factor ¼ C = C’ D’ E’ A’ B’ 2

Example Describe the dilation (from red to blue): Type of Dilation? Enlargement A = A’ B’ B C C’ 6 3 Center? A Scale Factor 3

Example Find the scale factor - the dashed image is a dilation of the solid image:

Example Find the scale factor - the dashed figure is a dilation image of the solid figure:

Example Draw the image of each figure under a dilation centered at the origin with the given scale factor:

Example Draw the image of each figure under a dilation centered at the origin with the given scale factor:

Example Find the image of figure LMNO under a dilation centered at the origin with the given scale factor: 1. Scale Factor of 2 L = (-6, -6) M = (-3, 0) N = (6, -3) O = (0, -3) L’ = (-12, -12) M’ = (-6, 0) N’ = (12, -6) O’ = (0, -6)

Example Find the image of figure LMNO under a dilation centered at the origin with the given scale factor: 1. Scale Factor of 1/3 L = (-6, -6) M = (-3, 0) N = (6, -3) O = (0, -3) L’ = (-2, -2) M’ = (-1, 0) N’ = (2, -1) O’ = (0, -1)

Homework: p. 676 1-17, 28-30