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  1. 1. Rotations About the Origin By Ishaq Chowdhury
  2. 2. Transformations can be pretty confusing Reflection? Dilation?
  3. 3. Especially when it comes to Rotations
  4. 4. Clockwise Rotation
  5. 5. But maybe I can help explain it
  6. 6. Let’s Start With a Definition A rotation about a point “P” through an angle, “X” is a transformation such that: 1. the image of P is P 2. Any other point Q has the point Q’, where PQ=PQ’ and <QPQ’=X
  7. 7. What does that even mean? In simple english it means that everything moves except the point you’re rotating around. All the points move in a way that it stays the same distance from center of the rotation as it did before.
  8. 8. Usually a rotation occurs with the origin at the center. Here are some rules for the most used rotations.
  9. 9. A 90 degrees counter- clockwise rotation is: R90(x, y) to (-y, x) The x coordinate and the y coordinate switch places and the y is negated.
  10. 10. A 180 degrees counter-clockwise rotation is: R180(x, y) to (-x, -y) Both the x and the y coordinates are negated.
  11. 11. A 270 degrees counter-clockwise rotation is: R270(x, y) to (y, -x) The x coordinate and the y coordinate switch the the x is negated.
  12. 12. If a figure is rotated clockwise: The degrees of rotation becomes negative. For example: rotate 270 degrees clockwise R-270(x, y) This is the same as 90 degrees counter-clockwise rotation. so R-270(x, y) is (-y, x)
  13. 13. But when will we actually ever need to know how to rotate things in real life?
  14. 14. Let’s think: Counter-CLOCKwise
  15. 15. The hands of a clock rotate around the center to indicate what time it is.
  16. 16. Lets say we have our clock here. The center of the clock is at the origin. The point of the hour hand is at (0,2)
  17. 17. Rotating it 270 degrees would make it 3 o’clock. Applying the rule: R270(x, y)---(y, -x) would change (0,2) to (2, 0)
  18. 18. Rotating it 180 degrees from its original point would make it 6 o’clock. Applying the rule: R180(x, y)---(-x, -y) would change (0,2) to (0,-2)
  19. 19. Rotating it 90 degrees would make it 9’clock. Applying the rule: R90(x, y)---(-y, x) would change (0,2) to (-2,0)
  20. 20. Now you have the final piece of information that you need to rule the world!!!!! Congrats!