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Math Help - Rectangle rotation

  1. #1
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    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.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by Turtlebread View Post
    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.
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  3. #3
    Senior Member JaneBennet's Avatar
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    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).
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