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Rotations on a Coordinate Plane: Discovering the Rules with TED

Learn about rotations on a coordinate plane with TED. Explore the direction of rotations and understand the formulas for 90° and 180° rotations, both clockwise and counterclockwise. Use TED's eye coordinates to identify the rules for rotations.

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Rotations on a Coordinate Plane: Discovering the Rules with TED

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  1. Transformations: Rotations on a Coordinate Plane Meet TED. TED is going to help us learn about rotations. First let’s focus on TED’s eyes. What are the coordinates of his left eye? What are the coordinates of his right eye? Good, now you will need to use those coordinates in order to help you discover to rules for rotations.

  2. Before we go any further lets discuss the direction in which we rotate. Remember that our coordinate plane is broken into quadrants numbers 1 – 4. When we rotate we always go in order of quadrant unless told otherwise.

  3. A full rotation is 360° so if you rotate halfway around that would be a _____° rotation. A 90° rotation moves of the way around, which just means it moves one quadrant counter-clockwise. If you rotated a figure 90° from quadrant 4 it would then be in quadrant ______.

  4. ROTATIONS basic rotations

  5. A (-4,2) B (-7,7) C(-3,9) A’ (2,4) B’ (7,7) C’(9,3) A’ ( , ) B’ ( , ) C’( , )

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

  7. 90 clockwise rotation Formula (x, y)  (y, x) A(-2, 4) A’(4, 2)

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

  9. 90 counter-clockwise rotation Formula (x, y)  (y, x) A’(2, 4) A(4, -2)

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

  11. 180 rotation Formula (x, y)  (x, y) A’(4, 2) A(-4, -2)

  12. Rotate (3, -4) 180 Formula (x, y)  (x, y) (-3, 4) (3, -4)

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

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

  15. 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)

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

  17. Rotation Example Rotate ABC 270 clockwise. Formula? B(-2, 4) We must use the counterclockwise formula for 90, because 270 clockwise, is the same as 90  counterclockwise. A(-3, 0) C(1, -1) (x, y)  (y, x)

  18. Rotate ABC 270 clockwise, or 90 counterclockwise. 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) C’ C(1, -1) A(-3, 0) B’ A’

  19. Rotation Formulas • 90 CW (x, y)  (y, x) • 90 CCW (x, y)  (y, x) • 180 (x, y)  (x, y)

  20. http://www.ixl.com/math/grade-8/rotations-graph-the-image

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