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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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**This dilation is an enlargement . Corresponding distances**

Image Distance 4 2 = = 2 = k Scale Factor Original Distance 2 > 1 This dilation is an enlargement . Corresponding distances

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**This dilation is an reduction. Corresponding distances**

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

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Example: Rectangle W’X’Y’Z’ is the image of rectangle WXYZ after a dilation. Find the scale factor of the dilation. 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?**

K = 4 K = ½ K = 1 4>1 Enlargement ½ <1 Reduction Congruent

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**Matching K = ¼ K = 3 Reduction K = 2/7 Enlargement K = 1 K = 5**

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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