geometry

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In the xy - plane, line l has equation y= -x. Point P lies on l and has coordinates (-2,2). If l is rotated counterclockwise 45 degrees about the origin, what will be the coordinates of the image of P under this rotation.

  • geometry -

    Recall your rotation matrix.
    (x,y) -> (x',y') where

    x' = xcosθ - ysinθ
    y' = xsinθ + ycosθ

    So, plug in your θ.

    You can easily check your work by noting that the point will rotate down to the x-axis.

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