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Notes Dilations

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Definitions Dilation - a transformation in which every point P has an image P' placed on OP so that and OP' = k * OP Center of Dilation – the point from which an original figure is dilated. Scale Factor - the ratio of the image length to the corresponding original length.

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Scale Factor If the scaled factor is greater than 1, then it is an enlargement (k>1). If the scaled factor is equal to 1, then it is a congruent figure (k=1) If the scale factor is less than 1, then it is a reduction (k<1).

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Corresponding distances 4242 = = 2 Image Distance Original Distance = k Scale Factor 2 > 1 This dilation is an enlargement.

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Corresponding distances 2323 = Image Distance Original Distance = k Scale Factor 2/3 < 1 This dilation is an reduction.

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Example: 1.Rectangle W’X’Y’Z’ is the image of rectangle WXYZ after a dilation. a.Find the scale factor of the dilation. b.Tell whether the image is a reduction or an enlargement.

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Example: 2.

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Example: 3.

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Reduction, Enlargement, or Congruent? 1.K = 4 2.K = ½ 3.K = 1 4>1 Enlargement ½ <1 Reduction Congruent

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Matching A.K = ¼ B.K = 3 C.K = 2/7 D.K = 1 E.K = 5 F.K = 3/8 Reduction Enlargement Congruent

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7. scale factor 2

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8. scale factor ¼

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8. scale factor 1/3

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