How to calculate new position of a rectangle after translation and rotation?

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I have a rectangle - lets say 100 long by 75 high. Origin been bottom left corner. I move the rectangle up and across by 10 and rotate by 3 degrees from centre of part. How do I calculate the new position of the origin in X and Y.

I need to make only 3 measurements: 2 from X direction, and 1 from Y. I will use a laser to get 3 master measurements. I will move part and re-measure from same positions. I can compare new measurements to original but do not know to calculate.