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# Rotations

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• 1. Rotations About the Origin By Ishaq Chowdhury
• 2. Transformations can be pretty confusing Reflection? Dilation?
• 3. Especially when it comes to Rotations
• 4. Clockwise Rotation
• 5. But maybe I can help explain it
• 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. 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. Usually a rotation occurs with the origin at the center. Here are some rules for the most used rotations.
• 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. A 180 degrees counter-clockwise rotation is: R180(x, y) to (-x, -y) Both the x and the y coordinates are negated.
• 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. 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. But when will we actually ever need to know how to rotate things in real life?
• 14. Let’s think: Counter-CLOCKwise
• 15. The hands of a clock rotate around the center to indicate what time it is.
• 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. 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. 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. 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. Now you have the final piece of information that you need to rule the world!!!!! Congrats!