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How to do rotations around a given point?
Hi I am trying to learn this concept for my precalc class. We will be having a quiz soon. I know how to do rotations around the center, but I dont know how to do this around a given point. I know it has something to do with moving the center to the point, doing the rotation then moving it back. But couls someone please explain this to me? Thanks
1 Answer
- Anonymous7 years agoFavorite Answer
No, you move the POINT and everything else to the center by subtracting the point's coordinates from every point you wish to rotate, you apply the rotation, then you add the point's original coordinates back to everything.
As you know, the location of the point is determined by the vector that points to the point, which is (P1-0, P2-0), as a result, if you subtract (P1, P2) from everything, it'll be pushed into the (0,0) central point, where rotation can be applied.
Rotation is applied via the formula:
x' = x*cos(alpha) - y*sin(alpha)
y' = x*sin(alpha) + y*cos(alpha)