# How to find a new point on rectangle based on an known point on the same?

I have rotated a rectangle a certain amount of degree and got the point(x,y)=(130,40) which was previously (152,60). Now i want to find the x,y(marked as red) value at another location based on the known value (130,40) of the rotated rectangle.

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It does not look like we have enough information to deduce a specific point $(x,y)$ as indicated. Maybe you have a location on the original rectangle in mind. –  Karl Kronenfeld Apr 24 '13 at 9:48
I have the revised location of (521,60) on the rotated rectangle which is (130,40). Angle is also another info. –  Max_dev Apr 24 '13 at 9:53

The transformation has the form $$(x,y)\mapsto (a+x\cos\alpha-y\sin\alpha,b+y\cos\alpha+x\sin\alpha)$$ where $\alpha$ is your rotating angle and $a,b$ determine the translational part (and can be obtained from one point and image point if $\alpha$ is known).