EXAMPLE 4

1. 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

2. 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

3. 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

4. 5. The vertices of RSTare R(1, 2), S(2, 1), and T(2, 2). Use scalar multiplication to find the vertices of R’S’T’ after a dilation with its center at the origin and a scale factor of 2. ANSWER R’(2,4), S’(4,2), T’(4,4) for Examples 4 and 5 GUIDED PRACTICE

5. 6. A segment has the endpoints C( –1, 1) and D(1, 1). Find the image of CDafter a 90° rotation about the origin followed by a dilation with its center at the origin and a scale factor of 2. ANSWER C’( 2, 2), D’( 2,2) for Examples 4 and 5 GUIDED PRACTICE