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Geometry/Rotating around points other than the origin?


I am very confused about how to rotate a shape around a point ther than the origin. The questions are usually like this "Rotation 90 degrees clockwise around 0,1".

I'd appreciate it if it could be answered today.

Thank you.

The point given will be taken to be (x,y).
Take the point and subtract 1 from the y coordinate, giving (x,y-1).
Convert (x,y-1) that to polar coordinates.
Add on however much of a rotation to the angle.
Convert that new point back to (x,y).

That is, suppose we had (4,4).
Subtracting 1 from y would gives us (4,3).
Converting to polar coordinates would give (5,arctan(4/3)).
A rotation of 90 degrees would add 90 to the angle, which would make it arctan(-3/4).
Conversion back to (x,y) would give(-3,4).
Adding back in the y would give (-3,5).


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Scott A Wilson


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