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Reflection of Polygon DEF in the Y-Axis Using Matrix Multiplication

Learn how to find the reflection of the polygon DEF, with vertices D(1, 2), E(3, 3), and F(4, 0), in the y-axis using matrix multiplication. We will guide you through the process step-by-step, from multiplying the polygon matrix by the reflection matrix to graphing the original shape and its image. This example will also help you understand how to reflect another polygon LMN, demonstrating both y-axis and x-axis reflections. Enhance your understanding of transformations using matrix methodologies.

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Reflection of Polygon DEF in the Y-Axis Using Matrix Multiplication

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  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

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