1. EXAMPLE 3 Use matrices to rotate a figure SOLUTION STEP 1Write the polygon matrix: 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 2Multiply by the matrix for a 180 rotation. o

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

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

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

5. GUIDED PRACTICE for Example 3 Use the quadrilateral EFGH in Example 3. Find the image matrix after the rotation about the origin. Graph the image. 3. 270°

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

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

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