# Dilations: (Stretching/Shrinking)

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Dilations: (Stretching/Shrinking). Dilations use a scale factor to reduce or enlarge shapes. Every dilation has a center and a scale factor. Most of the time it is the origin (0, 0) Scale Factor: tells you how many times larger or smaller your image will be. - PowerPoint PPT Presentation

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• Dilations: (Stretching/Shrinking)Dilations use a scale factor to reduce or enlarge shapes.Every dilation has a center and a scale factor. Most of the time it is the origin (0, 0)Scale Factor: tells you how many times larger or smaller your image will be.

The new shape and the image are similar. Dilations are also called similarity transformations.

• Finding a DilationTo find a dilation with center C and scale factor n, you can use the following two rules.The image C is itself (meaning C=C)For any point R, R is on CR and CR = nCR.

• How do we locate dilation images?A dilation is a transformation who preimage and image are similar. A dilation is not an isometry. Every dilation has a center and a scale factor n, n >0. The scale factor describes the size change from the original figure to the image.

• Example 1:Quadrilateral ABCD has vertices A(-2, -1), B(-2, 1), C(2, 1) and D(1, -1). Find the coordinates of the image for the dilation with a scale factor of 2 and center of dilation at the origin. ABCABCDD

• Example 2:F(-3, -3), O(3, 3), R(0, -3) Scale factor 1/3

FORFOR

• Example 3:T(-1, 0), H(1, 0), I(2, -2), S(-2, -2) Scale factor 4THITHISS

• The dilation is an enlargement if the scale factor is > 1.

The dilation is a reduction if the scale factor is between 0 and 1.

• Finding a Scale FactorThe blue triangle is a dilation image of the red triangle. Describe the dilation.

The center is X. The image is larger than the preimage, so the dilation is an enlargement.

• Finding a Scale FactorThe blue quadrilateral is a dilation image of the red quadrilateral. Describe the dilation.

• Graphing Dilation ImagesPZG has vertices P(2,0), Z(-1, ), and G (1, -2).What are the coordinates of the image of P for a dilation with center (0,0) and scale factor 3?

a) (5, 3)b) (6,0) c) (2/3, 0)d) (3, -6)

• Graphing Dilation ImagesSolution:The scale factor is 3, so use the rule:(x, y)(3x, 3y).P(2,0) P(32, 30) or P(6, 0). The correct answer is B.

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