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MA 08 Geometry

MA 08 Geometry. 6.9 Rotations. Goals. Identify rotations in the plane. Apply rotation formulas to figures on the coordinate plane. Rotation. A transformation in which a figure is turned about a fixed point, called the center of rotation. Center of Rotation. Rotation.

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MA 08 Geometry

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  1. MA 08 Geometry 6.9 Rotations

  2. Goals • Identify rotations in the plane. • Apply rotation formulas to figures on the coordinate plane. 6.9 Rotations

  3. Rotation • A transformation in which a figure is turned about a fixed point, called the center of rotation. Center of Rotation 6.9 Rotations

  4. Rotation • Rays drawn from the center of rotation to a point and its image form an angle called the angle of rotation. G 90 Center of Rotation G’ 6.9 Rotations

  5. Rotations on the Coordinate Plane • Know the translation formulas for: • 90 rotations • 180 rotations • clockwise & counter-clockwise Unless told otherwise, the center of rotation is the origin (0, 0). 6.9 Rotations

  6. 90 clockwise rotation Formula (x, y)  (y, x) A(-2, 4) A’(4, 2) 6.9 Rotations

  7. Rotate (-3, -2) 90 clockwise Formula (x, y)  (y, x) A’(-2, 3) (-3, -2) 6.9 Rotations

  8. 90 counter-clockwise rotation Formula (x, y)  (y, x) A’(2, 4) A(4, -2) 6.9 Rotations

  9. Rotate (-5, 3) 90 counter-clockwise Formula (x, y)  (y, x) (-5, 3) (-3, -5) 6.9 Rotations

  10. 180 rotation Formula (x, y)  (x, y) A’(4, 2) A(-4, -2) 6.9 Rotations

  11. Rotate (3, -4) 180 Formula (x, y)  (x, y) (-3, 4) (3, -4) 6.9 Rotations

  12. Rotation Example B(-2, 4) Draw a coordinate grid and graph: A(-3, 0) B(-2, 4) C(1, -1) Draw ABC A(-3, 0) C(1, -1) 6.9 Rotations

  13. Rotation Example B(-2, 4) Rotate RST 90 clockwise. Formula (x, y)  (y, x) A(-3, 0) C(1, -1) 6.9 Rotations

  14. Rotate ABC 90 clockwise. B(-2, 4) (x, y)  (y, x) A(-3, 0)  A’(0, 3) B(-2, 4)  B’(4, 2) C(1, -1)  C’(-1, -1) A’ B’ A(-3, 0) C’ C(1, -1) 6.9 Rotations

  15. Rotate ABC 90 clockwise. B(-2, 4) Check by rotating ABC 90. A’ B’ A(-3, 0) C’ C(1, -1) 6.9 Rotations

  16. C B D A E H F G Rotating segments O 6.9 Rotations

  17. CE C B D A E H F G Rotating AC 90 CW about the origin maps it to _______. O 6.9 Rotations

  18. FE C B D A E H F G Rotating HG 90 CCW about the origin maps it to _______. O 6.9 Rotations

  19. ED C B D A E H F G Rotating AH 180 about the origin maps it to _______. O 6.9 Rotations

  20. GH C B D A E H F G Rotating GF 90 CCW about point G maps it to _______. O 6.9 Rotations

  21. C C B D A E A E H F G G Rotating ACEG 180 about the origin maps it to _______. EGAC O 6.9 Rotations

  22. C B D A E H F G Rotating FED 270 CCW about point D maps it to _______. BOD O 6.9 Rotations

  23. Practice Practice Practice 6.9 Rotations

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