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Warm Up

Warm Up 1. Translate the triangle with vertices A (2, –1), B (4, 3), and C (–5, 4) along the vector <2, 2>. A' (4,1), B' (6, 5), C (–3, 6). 2. ∆ ABC ~ ∆ JKL . Find the value of JK. Objective. Identify and draw dilations.

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Warm Up

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  1. Warm Up 1. Translate the triangle with vertices A(2, –1), B(4, 3), and C(–5, 4) along the vector <2, 2>. A'(4,1), B'(6, 5),C(–3, 6) 2. ∆ABC ~ ∆JKL. Find the value of JK.

  2. Objective Identify and draw dilations.

  3. Recall that a dilation is a transformation that changes the size of a figure but not the shape. The image and the preimage of a figure under a dilation are similar.

  4. Example 1: Identifying Dilations Tell whether each transformation appears to be a dilation. Explain. A. B. No; the figures are not similar. Yes; the figures are similar and the image is not turned or flipped.

  5. Helpful Hint 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. A dilation enlarges or reduces all dimensions proportionally. A dilation with a scale factor greater than 1 is an enlargement, or expansion. A dilation with a scale factor greater than 0 but less than 1 is a reduction, or contraction.

  7. If the scale factor of a dilation is negative, the preimage is rotated by 180°. For k > 0, a dilation with a scale factor of –k is equivalent to the composition of a dilation with a scale factor of k that is rotated 180° about the center of dilation.

  8. The dilation of (x, y) is Example 4: Drawing Dilations in the Coordinate Plane 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.

  9. The dilation of (x, y) is Check It Out! Example 4 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 .

  10. Assignment Pg. 653 (2-32 even)

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