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Holt Geometry 12-7 Dilations 12-7 Dilations Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz

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Holt Geometry 12-7 Dilations Warm Up 1. Translate the triangle with vertices A(2, –1), B(4, 3), and C(–5, 4) along the vector. 2. ∆ABC ~ ∆JKL. Find the value of JK. A'(4,1), B'(6, 5),C(–3, 6)

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Holt Geometry 12-7 Dilations Identify and draw dilations. Objective

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Holt Geometry 12-7 Dilations center of dilation enlargement reduction Vocabulary

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Holt Geometry 12-7 Dilations 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.

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Holt Geometry 12-7 Dilations Example 1: Identifying Dilations Tell whether each transformation appears to be a dilation. Explain. A. B. Yes; the figures are similar and the image is not turned or flipped. No; the figures are not similar.

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Holt Geometry 12-7 Dilations Check It Out! Example 1 a.b. Yes, the figures are similar and the image is not turned or flipped. No, the figures are not similar. Tell whether each transformation appears to be a dilation. Explain.

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Holt Geometry 12-7 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°. Helpful Hint

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Holt Geometry 12-7 Dilations

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Holt Geometry 12-7 Dilations 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.

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Holt Geometry 12-7 Dilations Example 2: Drawing Dilations Copy the figure and the center of dilation P. Draw the image of ∆WXYZ under a dilation with a scale factor of 2. Step 1 Draw a line through P and each vertex. Step 2 On each line, mark twice the distance from P to the vertex. Step 3 Connect the vertices of the image. W’W’X’X’ Z’Z’ Y’Y’

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Holt Geometry 12-7 Dilations Check It Out! Example 2 Copy the figure and the center of dilation. Draw the dilation of RSTU using center Q and a scale factor of 3. Step 1 Draw a line through Q and each vertex. Step 2 On each line, mark twice the distance from Q to the vertex. Step 3 Connect the vertices of the image. R’R’ S’S’ T’T’ U’U’

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Holt Geometry 12-7 Dilations Example 3: Drawing Dilations 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. The scale factor in the dilation is 4, so a 1 in. by 1 in. square of the actual flower is represented by a 4 in. by 4 in. square on the sketch. Let the actual diameter of the flower be d in. 3 = 4d d = 0.75 in.

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Holt Geometry 12-7 Dilations Check It Out! Example 3 What if…? 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. The scale factor of the dilation is 4, so a 10 in. by 10 in. square on the photograph represents a 40 in. by 40 in. square on the painting. Find the area of the painting. A = l w = 4(10) 4(10) = 40 40 = 1600 in 2

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Holt Geometry 12-7 Dilations

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Holt Geometry 12-7 Dilations 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.

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Holt Geometry 12-7 Dilations 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. The dilation of (x, y) is

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Holt Geometry 12-7 Dilations Example 4 Continued Graph the preimage and image. P’ Q’ R’ P R Q

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Holt Geometry 12-7 Dilations 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. The dilation of (x, y) is

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Holt Geometry 12-7 Dilations Check It Out! Example 4 Continued Graph the preimage and image. R S T U R’ S’ T’ U’

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Holt Geometry 12-7 Dilations Lesson Quiz: Part I 1. Tell whether the transformation appears to be a dilation. yes 2. Copy ∆RST and the center of dilation. Draw the image of ∆RST under a dilation with a scale of.

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Holt Geometry 12-7 Dilations 3. A rectangle on a transparency has length 6cm and width 4 cm and with 4 cm. On the transparency 1 cm represents 12 cm on the projection. Find the perimeter of the rectangle in the projection. Lesson Quiz: Part II 4. 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. 240 cm

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