EXAMPLE 5

1. The vertices of DEFare D(1, 2), E(3, 3), and F(4, 0). Find the reflection of DEFin the y-axis using matrix multiplication. Graph DEFand its image. D E F Multiply the polygon matrix by the matrix for a reflection in the y-axis. –1 0 1 3 4 STEP 1 + 0 1 2 3 0 Polygon matrix Reflection matrix EXAMPLE 5 Use matrix multiplication to reflect a polygon SOLUTION

2. –1(1) + 0(2) –1(3) + 0(3) –1(4) + 0(0) = 0(1) + 1(2) 0(3) + 1(3) 0(4) + 1(0) D′ E′ F′ –1 –3 –4 = 2 3 0 Image matrix EXAMPLE 5 Use matrix multiplication to reflect a polygon

3. EXAMPLE 5 Use matrix multiplication to reflect a polygon STEP 2 GraphDEFandD′E′F′.

4. The vertices ofLMN areL(–3, 3), M(1, 2),andN(–2, 1). reflection using matrix multiplication. Find the described Multiply the polygon matrix by the matrix for a reflection in the y-axis. STEP 1 for Example 5 GUIDED PRACTICE 7. Reflect LMNin the x-axis. SOLUTION

5. L M N 1 0 1(–3 ) + 0(3) 1(1) + 0(2) –3 1 –2 1(–2) + 0(1) = 0(–3 ) + –1(3) 0(1) + –1(2) 0(–2) + –1(1) 0 –1 3 2 1 Polygon matrix Reflection matrix L′ M′ N′ –3 1 –2 = –3 –2 –1 Image Matrix for Example 5 GUIDED PRACTICE

6. The vertices ofLMN areL(–3, 3), M(1, 2),andN(–2, 1). reflection using matrix multiplication. Find the described Multiply the polygon matrix by the matrix for a reflection in the x-axis. STEP 1 for Example 5 GUIDED PRACTICE 8. Reflect LMNin the y-axis. SOLUTION

7. L M N –1 0 –1(–3 ) + 0(3) –1 (1) + 0(2) –1(–2) + 0(1) = 0(–3 ) + 1(3) 0(1) + 1(2) 0(–2) + 1(1) 0 1 3 2 1 Polygon matrix Reflection matrix L′ M′ N′ 3 –1 2 = 3 2 1 Image Matrix for Example 5 GUIDED PRACTICE –3 1 –2