1. 12-5 Graphing Rotations Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

2. Warm Up Parallelogram ABCD has vertices (-4, 1), (0, 1), (–3, 4), and (1, 4). 1. What are the vertices of ABCD after it has been reflected across the x-axis? 2. What are the vertices after is has been reflected across the y-axis? (–4, –1), (0, –1), (–3, –4), (1, –4) (4, 1), (0, 1), (3, 4), (–1, 4) Course 1 12-5 Graphing Rotations

3. Problem of the Day If each of the capital letters of the alphabet is rotated a half turn around its center, which will look the same? H, I, N, O, S, X, Z Course 1 12-5 Graphing Rotations

4. Learn to use rotations to change positions of figures on a coordinate plane. Course 1 12-5 Graphing Rotations

5. You can rotate a figure about the origin or another point on a coordinate plane. Course 1 12-5 Graphing Rotations

6. A rotation is the movement of a figure about a point. Rotating a figure “about the origin” means that the origin is the center of rotation. Remember! Course 1 12-5 Graphing Rotations

7. -8 -6 -4 -2 2 4 6 8 8 2 4 6 -2 -4 -6 -8 y x Additional Example 1: Rotating Figures on a Coordinate Plane EF GH Course 1 12-5 Graphing Rotations Give the coordinates of the vertices of the figure after the given rotation. Rotate parallelogram EFGH clockwise 90° about the origin.

8. Additional Example 1 Continued The new x-coordinates are the old y-coordinates. The new y-coordinates are the opposites of the old x-coordinates. EFGHE’F’G’H’ E(–4, 0)E’(0, 4) F(0, 0)F’(0, 0) G(–2, –3)G’(–3, 2) H(–6, –3)H’(–3, 6) Course 1 12-5 Graphing Rotations

9. Additional Example 1 Continued Rotate parallelogram EFGH 90° about the origin. -8 -6 -4 -2 2 4 6 8 8 2 4 6 -2 -4 -6 -8 y x E F GH F’F’ E’E’ G’G’ H’H’ Course 1 12-5 Graphing Rotations

10. -8 -6 -4 -2 2 4 6 8 8 2 4 6 -2 -4 -6 -8 y x Try This: Example 1 Give the coordinates of the vertices of the figure after the given rotation. Rotate parallelogram EFGH counterclockwise 180° about the origin. EF GH Course 1 12-5 Graphing Rotations

11. Try This: Example 1 Continued The new x-coordinates are the opposites of the old x-coordinates. The new y-coordinates are the opposites of the old y-coordinates. EFGHE’F’G’H’ E(–4, 0)E’(4, 0) F(0, 0)F’(0, 0) G(–2, –3)G’(2, 3) H(–6, –3)H’(6, 3) Course 1 12-5 Graphing Rotations

12. -8 -6 -4 -2 2 4 6 8 8 2 4 6 -2 -4 -6 -8 y x Try This: Example 1 Continued Rotate parallelogram EFGH counterclockwise 180° about the origin. EF GH E’F’F’ G’G’ H’H’ Course 1 12-5 Graphing Rotations

13. Additional Example 2A: Art Application An artist draws this figure. She rotates the figure without changing its size or shape. Give the coordinates of the vertices of the figure after a clockwise rotation of 90° about the origin. -8 -6 -4 -2 2 4 6 8 8 2 4 6 -2 -4 -6 -8 y x C D B A E Course 1 12-5 Graphing Rotations

14. ABCDEA’B’C’D’E’ A(0, 0)A’(0, 0) B(1, 4)B’(4, –1) C(3, 5)C’(5, –3) D(7, 3)D’(3, –7) Additional Example 2A Continued E(6, 0)E’(0, –6) The new x-coordinates are the old y-coordinates. The new y-coordinates are the opposites of the old x-coordinates. Course 1 12-5 Graphing Rotations

15. Additional Example 2A Continued Rotate the figure after a clockwise 90° about the origin. -8 -6 -4 -2 2 4 6 8 8 2 4 6 -2 -4 -6 -8 y x C D B A E C’C’ D’D’ B’B’ A’A’ E’E’ Course 1 12-5 Graphing Rotations

16. B. Give the coordinates of the vertices of the figure after a counterclockwise rotation of 180° about the origin. Additional Example 2B: Art Application -8 -6 -4 -2 2 4 6 8 8 2 4 6 -2 -4 -6 -8 y x C D B A E Course 1 12-5 Graphing Rotations

17. The new x-coordinates are the opposites of the old x-coordinates. The new y-coordinates are the opposites of the old y-coordinates. Additional Example 2B Continued ABCDEA’B’C’D’E’ A(0, 0)A’(0, 0) B(1, 4)B’(–1, –4) C(3, 5)C’(–3, –5) D(7, 3)D’(–7, –3) E(6, 0)E’(–6, 0) Course 1 12-5 Graphing Rotations

18. Additional Example 2B Continued Rotate the figure after a clockwise 180° about the origin. -8 -6 -4 -2 2 4 6 8 8 2 4 6 -2 -4 -6 -8 y x C D B A E C’C’ D’D’ B’B’ A’A’E’E’ Course 1 12-5 Graphing Rotations

19. Try This: Example 2A An artist draws this figure. She rotates the figure without changing its size or shape. Give the coordinates of the vertices of the figure after a clockwise rotation of 90° about the origin. -8 -6 -4 -2 2 4 6 8 8 2 4 6 -2 -4 -6 -8 y x C D B A E Course 1 12-5 Graphing Rotations

20. ABCDEA’B’C’D’E’ A(–6, 0)A’(0, 6) B(–5, 4)B’(4, 5) C(–3, 5)C’(5, 3) D(1, 3)D’(3, –1) Try This: Example 2A Continued E(0, 0)E’(0, 0) The new x-coordinates are the old y-coordinates. The new y-coordinates are the opposites of the old x-coordinates. Course 1 12-5 Graphing Rotations

21. Try This: Example 2A Continued Rotate the figure after a clockwise 90° about the origin. -8 -6 -4 -2 2 4 6 8 8 2 4 6 -2 -4 -6 -8 y x C D B A E C’C’ D’D’ B’B’ A’A’ E’E’ Course 1 12-5 Graphing Rotations

22. B. Give the coordinates of the vertices of the figure after a counterclockwise rotation of 180° about the origin. Try This: Example 2B -8 -6 -4 -2 2 4 6 8 8 2 4 6 -2 -4 -6 -8 y x C D B A E Course 1 12-5 Graphing Rotations

23. The new x-coordinates are the opposites of the old x-coordinates. The new y-coordinates are the opposites of the old y-coordinates. Try This: Example 2B Continued ABCDEA’B’C’D’E’ A(–6, 0)A’(6, 0) B(–5, 4)B’(5, –4) C(–3, 5)C’(3, –5) D(1, 3)D’(1, –3) E(0, 0)E’(0, 0) Course 1 12-5 Graphing Rotations

24. Try This: Example 2B Continued Rotate the figure after a clockwise 180° about the origin. -8 -6 -4 -2 2 4 6 8 8 2 4 6 -2 -4 -6 -8 y x C D B A E C’C’ D’D’ B’B’ A’A’ E’E’ Course 1 12-5 Graphing Rotations

25. Lesson Quiz Give the coordinates of the vertices of the trapezoid after the given rotation. 1. Rotate trapezoid ABCD counterclockwise 180° about the origin. 2. Rotate trapezoid ABCD clockwise 90° about the origin. A’(0, 5), B’(0, 0), C’(–3, 1), D’(–3, 4) A’(5, 0), B’(0, 0), C’(1, 3), D’(4, 3) Insert Lesson Title Here Course 1 12-5 Graphing Rotations