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Geometry

Geometry. Section 9.7. a. Because = , the scale factor is k = . The image P’ is an enlargement. a. CP’. 12. 3. CP. 8. 2. EXAMPLE 1. Identify dilations. Find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement.

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Geometry

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  1. Geometry Section 9.7

  2. a. Because = , the scale factor is k = . The image P’ is an enlargement. a. CP’ 12 3 CP 8 2 EXAMPLE 1 Identify dilations Find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement. SOLUTION

  3. b. b. Because = , the scale factor is k = . The image P’ is a reduction. CP’ 3 CP 5 18 30’ EXAMPLE 1 Identify dilations Find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement. SOLUTION

  4. Draw and label DEFG. Then construct a dilation of DEFGwith point Das the center of dilation and a scale factor of 2. EXAMPLE 2 Draw a dilation SOLUTION STEP 1 Draw DEFG. Draw rays from Dthrough vertices E, F, and G.

  5. Open the compass to the length of DE. Locate E’ on DEsoDE’ = 2(DE). Locate F’ and G’ the same way. EXAMPLE 2 Draw a dilation STEP 2

  6. EXAMPLE 2 Draw a dilation STEP 3 Add a second label D’ to point D. Draw the sides ofD’E’F’G’.

  7. Assignment 1 of 2 • #3-13 odd, page 629

  8. Simplify the product: 4 [ ] 4(3) 4(0) 4(1) = 4 4(2) 4(– 1) 4(– 3) [ ] [ ] [ ] 12 0 4 3 0 1 3 0 1 = 8 – 4 –12 2 – 1 – 3 2 – 1 – 3 EXAMPLE 3 Scalar multiplication SOLUTION Multiply each element in the matrix by 4. Simplify.

  9. The vertices of quadrilateral KLMNare K(– 6, 6), L(– 3,6), M(0, 3), and N(– 6, 0). Use scalar multiplication to find the image of KLMNafter a dilation with its center at the origin and a scale factor of . Graph KLMNand its image. K L M N K’ L’ M’ N’ [ ] [ ] – 2 – 1 0 – 2 2 2 1 0 = 1 1 3 3 Image matrix Scale factor Polygon matrix – 6 – 3 0 – 6 6 6 3 0 EXAMPLE 4 Use scalar multiplication in a dilation SOLUTION

  10. The vertices of ABCare A(– 4, 1),B(– 2, 2), and C( – 2,1). Find the image of ABCafter the given composition. Translation: (x, y) (x + 5, y + 1) Dilation: centered at the origin with a scale factor of 2 STEP 1 Graph the preimage ABCon the coordinate plane. EXAMPLE 5 Find the image of a composition SOLUTION

  11. STEP 2 Translate ABC5 units to the right and 1 unit up. Label it A’B’C’. STEP 3 Dilate A’B’C’using the origin as the center and a scale factor of 2 to find A”B”C”. EXAMPLE 5 Find the image of a composition

  12. Assignment 2 of 2 • #15-25 odd, pages 629 & 630

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