Understanding Rotations on the Coordinate Plane

Rotations on the coordinate plane involve turning points either clockwise or counterclockwise around the origin. Different rotations like 90, 180, 270, and 360 degrees have specific rules and effects on the coordinates. It's important to know how to symbolically represent rotations and understand the differences between clockwise and counterclockwise rotations. Visual examples further illustrate these concepts.

• Rotations
• Coordinate Plane
• Counterclockwise
• Clockwise
• Transformations

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1. ROTATIONS ROTATIONS on the coordinate plane CENTERED AT THE ORIGIN (0,0)

2. Rotations are TURNS You can either turn counterclockwise(ccw) or clockwise(cw) TURNS If you are turning counterclockwise(ccw), then you are turning against the way the clock goes, which is to the left and your degree will be positive. If you are turning clockwise(cw), then you are turning with the clock hands, which is to the right and your degree will be negative.

3. There are 4 4 main ROTATIONS coordinate plane: Symbol for a Rotation is a capital R So, here are the rules, in words: Rotate 90 degrees about the origin, we switch x and y and change the sign of the new x. Rotate 180 degrees about the origin, we change BOTH signs only. This is the same as a POINT REFLECTION. Rotate 270 degrees about the origin, we switch x and y and change the sign of the new y. Rotate 360 degrees about the origin, we keep the point the same, because it s going full circle. ROTATIONS on the

4. These rules symbolically: R 1) (x,y) ( , ) y x 90 180 R 2) (x,y) ( , ) x y 3) (x,y) 270 R ( , ) y x 4) (x,y) R ( , ) x y 360

5. CCW - CW The following are equivalent angle rotations: = R R 1) 90 270 = R R 2) 180 180 = R R 3) 270 90

6. Rotation of 90 degrees CCW and 270 degrees CW

7. Rotation of 180 degrees CCW and 180 degrees CW

8. Rotation of 270 degrees CCW and 90 degrees CW