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Understanding Geometric Transformations: Dilation and Reduction Explained

Explore the concepts of geometric transformations, focusing on dilations and reductions. A dilation enlarges or reduces a shape while maintaining its proportions. Key components include the scale factor, which determines the extent of change, and the center of dilation, which serves as the reference point. Through practical examples involving triangles and other shapes, this guide illustrates how to perform dilations with various scale factors and centers. Learn to manipulate shapes through reflection and rotation in addition to dilation, enhancing your understanding of geometric transformations.

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Understanding Geometric Transformations: Dilation and Reduction Explained

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  1. Geometric Transformations Dilations & Reductions

  2. Definitions • Dilation: transformation that produces an image that is the same shape as the original, but a different size • Enlargement: image bigger than the preimage • Reduction: image smaller than the preimage • Scale factor: how much the preimage changes • Center of dilation: self explanatory—the center of the preimage/image

  3. Example Draw the dilation of ∆ABC with vertices A(-1,-1), B(0,2), C(1,-2), with the center of dilation at the origin and a scale factor of 3.

  4. Example Draw the dilation of ∆EFG with vertices E(0,0), F(0,6), G(8,0), center of dilation at E, and scale factor of ½ .

  5. Example Draw ABCD: A(1,1), B(5,1), C(1,5), D(5,5) Dilate by a scale factor of ½. Translate 3 up, 4 left. Reflect over the y-axis.

  6. Example Draw JKLM: J(2,-2), K(1,1), L(-2,-3), M(0,-5) Reflect over the y-axis. Rotate 180 degrees around the origin.

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