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EXAMPLE 3

Trapezoid EFGH has vertices E (–3, 2) , F (–3, 4) , G (1, 4) , and H (2, 2) . Find the image matrix for a 180 rotation of EFGH about the origin. Graph EFGH and its image. o. STEP 1. Write the polygon matrix:. o. STEP 2. Multiply by the matrix for a 180 rotation. EXAMPLE 3.

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EXAMPLE 3

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  1. Trapezoid EFGH has vertices E(–3, 2), F(–3, 4),G(1, 4), and H(2, 2). Find the image matrix for a 180 rotation of EFGH about the origin. Graph EFGHand its image. o STEP 1 Write the polygon matrix: o STEP 2 Multiply by the matrix for a 180 rotation. EXAMPLE 3 Use matrices to rotate a figure SOLUTION

  2. EXAMPLE 3 Use matrices to rotate a figure STEP 3 Graph the preimage EFGH. Graph the image E′F′G′H′.

  3. for Example 3 GUIDED PRACTICE Use the quadrilateral EFGH in Example 3. Find the image matrix after the rotation about the origin. Graph the image. 3. 90°

  4. E F G H E′ F′ G′ H′ 0 –1 –3 –3 1 2 –2 –4 –4 –2 = 1 0 2 4 4 2 –3 –3 1 2 Image Matrix Rotation matrix Polygon matrix for Example 3 GUIDED PRACTICE SOLUTION

  5. for Example 3 GUIDED PRACTICE Use the quadrilateral EFGH in Example 3. Find the image matrix after the rotation about the origin. Graph the image. 4.270°

  6. E F G H E′ F′ G′ H′ 0 1 –3 –3 1 2 2 4 4 2 = –1 0 2 4 4 2 –3 3 –1 –2 Image Matrix Rotation matrix Polygon matrix for Example 3 GUIDED PRACTICE SOLUTION

  7. for Example 3 GUIDED PRACTICE Use the quadrilateral EFGH in Example 3. Find the image matrix after the rotation about the origin. Graph the image. 5. 360°

  8. E F G H E′ F′ G′ H′ 1 0 –3 –3 1 2 3 –3 1 2 = 2 4 4 2 0 1 2 4 4 2 Image Matrix Rotation matrix Polygon matrix for Example 3 GUIDED PRACTICE SOLUTION

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