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12-5

Graphing Rotations. 12-5. Course 1. Warm Up. Problem of the Day. Lesson Presentation. Graphing Rotations. 12-5. Course 1. Warm Up Parallelogram ABCD has vertices (-4, 1), (0, 1), (–3, 4), and (1, 4).

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12-5

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

  2. Graphing Rotations 12-5 Course 1 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)

  3. Graphing Rotations 12-5 Course 1 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

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

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

  6. Graphing Rotations 12-5 Remember! 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. Course 1

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

  8. Graphing Rotations 12-5 The new x-coordinates are the old y-coordinates. The new y-coordinates are the opposites of the old x-coordinates. Course 1 Additional Example 1 Continued EFGH E’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)

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

  10. Graphing Rotations 12-5 y 8 6 4 2 x -8 -6 -4 -2 2 4 6 8 -2 -4 -6 -8 Course 1 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. E F H G

  11. Graphing Rotations 12-5 The new x-coordinates are the opposites of the old x-coordinates. The new y-coordinates are the opposites of the old y-coordinates. Course 1 Try This: Example 1 Continued EFGH E’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)

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

  13. Graphing Rotations 12-5 y 8 6 4 2 x -8 -6 -4 -2 2 4 6 8 -2 -4 -6 -8 Course 1 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. C B D E A

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

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

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

  17. Graphing Rotations 12-5 The new x-coordinates are the opposites of the old x-coordinates. The new y-coordinates are the opposites of the old y-coordinates. Course 1 Additional Example 2B Continued ABCDE A’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)

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

  19. Graphing Rotations 12-5 y 8 6 4 2 x -8 -6 -4 -2 2 4 6 8 -2 -4 -6 -8 Course 1 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. C B D E A

  20. Graphing Rotations 12-5 The new x-coordinates are the old y-coordinates. The new y-coordinates are the opposites of the old x-coordinates. Course 1 Try This: Example 2A Continued ABCDE A’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) E(0, 0) E’(0, 0)

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

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

  23. Graphing Rotations 12-5 The new x-coordinates are the opposites of the old x-coordinates. The new y-coordinates are the opposites of the old y-coordinates. Course 1 Try This: Example 2B Continued ABCDE A’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)

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

  25. Graphing Rotations 12-5 Course 1 Insert Lesson Title Here 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’(5, 0), B’(0, 0), C’(1, 3), D’(4, 3) A’(0, 5), B’(0, 0), C’(–3, 1), D’(–3, 4)

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