EXAMPLE 5 Use matrix multiplication to reflect a polygon

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

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

EXAMPLE 5 Use matrix multiplication to reflect a polygon STEP 2 Graph DEF and D′E′F′.

GUIDED PRACTICE for Example 5 The vertices of LMN are L(–3, 3), M(1, 2), and N(–2, 1). reflection using matrix multiplication. Find the described 7. Reflect LMN in the x-axis. SOLUTION STEP 1 Multiply the polygon matrix by the matrix for a reflection in the y-axis.

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

GUIDED PRACTICE for Example 5 The vertices of LMN are L(–3, 3), M(1, 2), and N(–2, 1). reflection using matrix multiplication. Find the described 8. Reflect LMN in the y-axis. SOLUTION STEP 1 Multiply the polygon matrix by the matrix for a reflection in the x-axis.

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