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Understanding Dilations in Geometry

This lesson focuses on dilations, a type of nonrigid transformation, where the image and preimage of a figure are similar. Learn how to identify dilations, find their scale factors, and apply them in real-life scenarios.

matthewcurtis
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Understanding Dilations in Geometry

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  1. Chapter 8 Similarity

  2. Section 7Dilations

  3. GOAL 1: Identifying Dilations In Chapter 7, you studied rigid transformations, in which the image and preimage of a figure are congruent. In this lesson, we will study a type of nonrigid transformation called a dilation, in which the image and preimage of a figure are similar.

  4. Example 1: Identifying Dilations Identify the dilation and find its scale factor.

  5. In a coordinate plane, dilations whose centers are the origin have the property that the image of P(x, y) is P’(kx, ky).

  6. Example 2: Dilation in a Coordinate Plane 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 ½. How does the perimeter of the preimage compare to the perimeter of the image? Perimeter of preimage = Perimeter of image =

  7. GOAL 2: Using Dilations in Real Life Example 3: Finding the Scale Factor

  8. Example 3: Finding the Scale Factor (continued) • LC = LP = 59 inches; LS = LH = 74 inches • LC = LP = 66 inches; LS = LH = 74 inches

  9. EXIT SLIP

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