# Math Help - Rectangle rotation

1. ## Rectangle rotation

Heya all,

I've got a problem where I know the four corners of a rectangle that is rotated about its center by an unknown angle. I need to know the angle of rotation, and also the width and height of the rectangle if it was not rotated at all.

For the life of me, I can't see how I can determine that information with just the four corners of the rectangle. Any help would be greatly appreciated.

Heya all,

I've got a problem where I know the four corners of a rectangle that is rotated about its center by an unknown angle. I need to know the angle of rotation, and also the width and height of the rectangle if it was not rotated at all.

For the life of me, I can't see how I can determine that information with just the four corners of the rectangle. Any help would be greatly appreciated.
I did not see this before.

Post the coordinates of the four corners so that we can play on your question.

3. Rotating about the origin by angle $\theta$ counterclockwise is the same by multiplying by the matrix $\begin{pmatrix}\cos\theta & -\sin\theta\\\sin\theta & \cos\theta\end{pmatrix}$.

So if the centre of your rectangle is the origin, if one corner of the rectangle has co-ordinates $(a,b)$, its co-ordinates after the rotation would be $(a\cos\theta-b\sin\theta,a\sin\theta+b\cos\theta)$.