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9-5 Dilations

9-5 Dilations. Dilation. A dilation is a copy of a figure that is larger or smaller than the original figure. The original figure and all dilations of it are similar. A dilation is an enlargement if the scale factor is greater than 1. The dilation will be LARGER than the original figure.

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9-5 Dilations

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  1. 9-5 Dilations

  2. Dilation • A dilation is a copy of a figure that is larger or smaller than the original figure. • The original figure and all dilations of it are similar. • A dilation is an enlargement if the scale factor is greater than 1. • The dilation will be LARGER than the original figure. • The dilation is a reduction if the scale factor is between 0 and 1. • The dilation will be SMALLER than the original figure.

  3. Finding a Scale Factor • ΔX’T’R’ is a dilation of ΔXTR. • Is the dilation an enlargement or a reduction? • What is the scale factor of the dilation?

  4. Finding the Coordinates of a Dilation • In this book, all dilations of a figure drawn in the coordinate plane has the origin as the center of dilation. • Therefore, you can find the coordinates of a dilation by multiplying the coordinates of the original figure by the scale factor. • You can also find the scale factor by dividing the coordinates of the dilation by the coordinates of the original figure.

  5. Finding a Dilation • What are the coordinates of each vertex of the dilation of ΔPZG if the center is (0, 0) and the scale factor is 2?

  6.  J’K’L’M’ is a dilation of JKLM with a center at (0, 0). Is the dilation an enlargement or reduction? What is the scale factor of the dilation?

  7. 9-6 Compositions of Reflections

  8. Compositions • A composition of transformations is a combination of two or more transformations, one after the other. • Theorem 9-1: A translation or rotation is a composition of two reflections.

  9. Glide Reflections • A glide reflection is the composition of a translation and a reflection. • What is the image of TEX for a glide reflection where the translation is (x, y)  (x, y – 5) and the line of reflection is x = 0? T(-5, 2), E(-1, 3), X(-2, 1)

  10. Classifying Isometries • There are only four isometries: • Each figure below is an isometry image of the figure at the right. What type of isometry maps the preimage to the image?

  11. Each figure below is an isometry image of the figure at the right. What type of isometry maps the preimage to the image?

  12. Lesson Check • The blue figure is a dilation of the black figure with center of dilation C. • Is the dilation an enlargement or reduction? • What is the scale factor of the dilation?

  13. Assignment • Page 578 #16, 18, 23-25, 37 • Page 589 #12-14, 31-33

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