Geometry Section 9.7.

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Presentation transcript:

Geometry Section 9.7

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

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

EXAMPLE 2 Draw a dilation Draw and label DEFG. Then construct a dilation of DEFG with point D as the center of dilation and a scale factor of 2. SOLUTION STEP 1 Draw DEFG. Draw rays from D through vertices E, F, and G.

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

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

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

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

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

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

EXAMPLE 5 Find the image of a composition STEP 2 Translate ABC 5 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”.

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