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12.7 Dilations

12.7 Dilations. Dilations. Dilation: A transformation that changes the size of a figure, but not the shape. The image and the preimage are similar. Examples:. Tell whether each transformation appears to b a dilation. Explain. Examples:.

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12.7 Dilations

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  1. 12.7 Dilations

  2. Dilations • Dilation: A transformation that changes the size of a figure, but not the shape. • The image and the preimageare similar

  3. Examples: • Tell whether each transformation appears to b a dilation. Explain.

  4. Examples: • Tell whether each transformation appears to be a dilation. Explain.

  5. Dilations: • For a dilation with scale factor k, if k > 0, the figure is not turned or flipped. If k < 0, the figure is rotated by 180°.

  6. Dilations:

  7. Enlargements/Reductions • Enlargement: (expansions) enlarges all dimensions proportionally. A dilation with a scale factor greater than 1. • Reduction: (contraction) reduces all dimensions proportionally. A dilation with a scale factor greater than 0, but less than 1.

  8. Examples: • On a sketch of a flower, 4 in. represent 1 in. on the actual flower. If the flower has a 3 in. diameter in the sketch, find the diameter of the actual flower.

  9. Examples: • An artist is creating a large painting from a photograph into square and dilating each square by a factor of 4. Suppose the photograph is a square with sides of length 10 in. Find the area of the painting.

  10. Dilations In The Coordinate Plane

  11. Negative Dilations • If the scale factor of a dilation is negative, the preimage is rotated by 180°.

  12. Examples: • Draw the image of the triangle with vertices P(-4, 4), Q(-2, -2), and R(4, 0) under a dilation with a scale factor of centered at the origin.

  13. Examples: • Draw the image of the triangle with vertices R(0, 0), S(4, 0), T(2, -2), and U(–2, –2) under a dilation centered at the origin with a scale factor of .

  14. Examples: • A rectangle on a transparency has length 6 cm and width. On the transparency 1 cm represents 12 cm on the projection. Find the perimeter of the rectangle in the projection.

  15. Examples: • Draw the image of the triangle with vertices E(2, 1), F (1, 2) and G(-2, 2) under a dilation with a scale factor of -2 centered at the origin.

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