Question

Rotations Help?

My applet thingy on FLVS for rotations does not run in opera and so can someone how to do rotations for 90 degrees counter clockwise, 90 degrees clockwise and 180 degrees rotation?

Answer 1

When a point (a, b) is rotated 90 degrees anti-clockwise about the origin it becomes (-b,a). That is, you swap the x and y coordinates and change the sign of the x-coordinate. If you remember just this you can do all other rotations in multiples of 90 degrees both clockwise (CW) and anti-clockwise (ACW).
Examples:
1) Rotate (2,5) anti-clockwise by 90 degrees: (-5, 2)
2) Rotate (2,5) anti-clockwise by 180 degrees: Do it in 2 steps: (2,5) rotated 90 degrees ACW becomes (-5, 2). (-5, 2) rotated 90 more degrees ACW becomes (-2, -5).
3) Rotate (2,5) anti-clockwise by 270 degrees: Do it in 3 steps: (2,5) rotated 90 degrees ACW becomes (-5, 2). (-5, 2) rotated 90 more degrees ACW becomes (-2, -5). (-2, -5) rotated 90 more degrees ACW becomes (5, -2).
4) Rotate (2,5) anti-clockwise by 360 degrees: This will make one full rotation and end up where it started at (2.5). But you can also rotate the previous answer we got for 270 degrees at (5, -2) further by 90 degrees and it will become (2, 5).

For clockwise rotation you can arrive at the same position by the appropriate amount of anti-clockwise rotation. For example, 90 degrees clockwise is same as 270 degrees anti-clockwise. 180 degrees clockwise is identical to 180 degrees anti-clockwise, etc.

Answer 2

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