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

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.Find the coordinates of the image only do not graph.

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. A'(4,1), B'(6, 5),C(–3, 6)

Holt Geometry 12-7 Dilations Definition: 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. Dilation is a non-Rigid transformation.

Holt Geometry 12-7 Dilations

Holt Geometry 12-7 Dilations

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

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.

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.

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

Holt Geometry 12-7 Dilations

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.

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.

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’

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’

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.

Holt Geometry 12-7 Dilations

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.

Holt Geometry 12-7 Dilations Example 3: 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

Holt Geometry 12-7 Dilations Example 3: 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

Holt Geometry 12-7 Dilations Example 3 Continued Graph the preimage and image. P’ Q’ R’ P R Q

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

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

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

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

Holt Geometry 12-7 Dilations 3. A rectangle on a transparency has length 6cm and width 4 cm. On the transparency 1 cm represents 12 cm on the projection. Find the perimeter of the rectangle in the projection. Homework 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.