# Rotate a figure with given coordinates

I'm sorry if my question in not for here and because it's so stupid. I have a function, which draws a rectangle - it takes 4 parameters - width and lenght and 2 for positioning it. However, this is not so important. What I want to do, is to rotate it. Can you please tell e what to do with the coordinates of the rectangle to rotate it for example with 45 degrees?

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what is the center of the rotation ? – lorenzo Nov 11 '12 at 22:54
The center of the figure – Faery Nov 11 '12 at 22:55
The center of the rectangle, you mean? – Rahul Nov 11 '12 at 23:42

After writing down the coordinates of the corners of your rectangle, you'll want to multiply the coordinates (technically, the vector) by the rotation matrix: $$\begin{pmatrix} cos \theta & -sin \theta\\ sin \theta & cos \theta \end{pmatrix}$$ $\theta$ is the angle you want to rotate the rectangle(counterclockwise).
So, if your coordinate is $(x,y)$, your rotated coordinate will be: $$(xcos\theta+ysin\theta, -xsin\theta + ycos\theta)$$