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We have a rectangle that is rotating by its center from $0$ to $360$ degrees. This rectangle rotation starts in $0$ degrees when we know all four rectangle points. We also know the angle we want to rotate the rectangle.

What I need is a formula for these points when rectangle is rotated.

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1 Answer

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When you rotate the point $(x,y)$ through an angle of $\theta$ (radians, not degrees) about the origin the new position is $$ (x \cos\theta - y \sin\theta\ , \quad x\sin\theta + y\cos\theta). $$

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If the center of the rectangle is not at the origin, translate the center to move it there, rotate, then translate back.

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