How do I find the centre of rotationof a polygon rotated about a centre other than the origin.

I would find the center of 2 sides, and use a square to come 90 degrees off the center of the 2 sides, the center will be where they intersect.

I would translate the coordinates so it is rotating about the origin.

galactus IS the math expert, probably speaking more your language.
Check this out:
Geometry Session 7, Part B: Rotation Symmetry