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Graphing Transformations 3

Graphing Transformations 3. Rotation – the motion of an object around a fixed point. Direction of rotation – can be clockwise or counter-clockwise. Centre of rotation – the fixed point around which the rotation takes place. Angle of rotation – the amount of rotation made . y. 4. 3.

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Graphing Transformations 3

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  1. Graphing Transformations 3 Rotation – the motion of an object around a fixed point

  2. Direction of rotation – can be clockwise or counter-clockwise

  3. Centre of rotation – the fixed point around which the rotation takes place

  4. Angle of rotation – the amount of rotation made

  5. y 4 3 360° 2 1 x -4 -3 -2 -1 1 2 3 4 -1 -2 centre of rotation -3 -4

  6. y 4 90° counter-clockwise 3 2 +90° 1 x -4 -3 -2 -1 1 2 3 4 -1 -2 270° clockwise -3 -270° -4

  7. y 4 3 180° counter-clockwise +180° 2 1 x -4 -3 -2 -1 1 2 3 4 -1 -2 180° clockwise -3 -180° -4

  8. 4 TOP OF PAGE 3 2 1 -4 -3 -2 -1 1 2 3 4 -1 -2 -3 -4 A rotation +90°

  9. 4 TOP OF PAGE 3 2 1 -4 -3 -2 -1 1 2 3 4 -1 -2 -3 -4 A rotation +180°

  10. 4 TOP OF PAGE 3 2 1 -4 -3 -2 -1 1 2 3 4 -1 -2 -3 -4 A rotation +270°

  11. Would the images be different if the figures had been rotated clockwise instead of counter-clockwise?

  12. 4 TOP OF PAGE 3 2 1 -4 -3 -2 -1 1 2 3 4 -1 -2 -3 -4 A rotation -90°

  13. Would the images be different if the figures had been rotated clockwise instead of counter-clockwise? A 90° clockwise rotation produces the same image as a 270° counter-clockwise rotation, and vice versa.

  14. y Coordinates C’ 4 A(0,1) B(2,3) C(4,2) D(3,0) D’ 3 B B’ C 2 A 1 A’ D x -4 -3 -2 -1 1 2 3 4 A’(-1,0) B’(-3,2) C’(-2,4) D’(0,3) -1 -2 -3 -4 A rotation +90° OR-270°

  15. What patterns do you see in the coordinates of the figure and its image? • x-coordinates and y-coordinates switched and the x-coordinates have the opposite sign

  16. y Coordinates 4 A(0,1) B(2,3) C(4,2) D(3,0) 3 B C 2 A 1 D x -4 -3 -2 -1 1 2 3 4 D’ A’(0,-1) B’(-2,-3) C’(-4,-2) D’(-3,0) -1 A’ -2 C’ -3 B’ -4 A rotation +180° OR -180°

  17. What patterns do you see in the coordinates of the figure and its image? • x-coordinates and y-coordinates have the opposite sign

  18. y Coordinates 4 A(0,1) B(2,3) C(4,2) D(3,0) 3 B C 2 A 1 D x -4 -3 -2 -1 1 2 3 4 A’ A’(1,0) B’(3,-2) C’(2,-4) D’(0,-3) -1 -2 B’ -3 D’ C’ -4 A rotation +270° OR -90°

  19. What patterns do you see in the coordinates of the figure and its image? • x-coordinates and y-coordinates switched and the y-coordinates have the opposite sign

  20. How are a figure and its rotation image alike? They are congruent. They have the same orientation. If ABCD is read clockwise, then A’B’C’D’ is read clockwise.

  21. Coordinates y 4 A 3 B D 2 1 x -4 -3 -2 -1 1 2 3 4 C -1 -2 -3 -4 Rotate ABCD -90°

  22. Coordinates y 4 3 2 1 A x B -4 -3 -2 -1 1 2 3 4 D -1 -2 -3 C -4 Rotate ABCD +270°

  23. Coordinates y 4 3 2 A 1 x -4 -3 -2 -1 1 2 3 4 -1 B D -2 C -3 -4 Rotate ABCD 180°

  24. y Coordinates 4 A(0,1) B(2,3) C(4,2) D(3,0) 3 B C 2 A 1 D x -4 -3 -2 -1 1 2 3 4 -1 -2 -3 -4 A rotation

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