# Getting point-coordinates after a rotation

I have two points p1 and p2 on a 2-dimensional graph, each having an x-coordinate and an y-coordinate. I want to rotate p2 by 60 degrees around p1, such that p1 is fixed in its position. So, how to know the new p2 coordinates (after rotation)? I think there's some relation between the line that connects p1 to p2 and the angle 60, but can't figure what is.

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Write the points in column vectors: $\begin{pmatrix} x\\y \end{pmatrix}$. Then
$P_2':=\begin{pmatrix} \cos\varphi & -\sin\varphi \\ \sin\varphi & \cos\varphi \end{pmatrix}\cdot (P_2-P_1) + P_1$
where choose $\varphi=\pm 60^\circ$ according which direction you want to rotate.
Yes, matrix multiplication, I could have expanded it. First reduced the problem where $P_1$ is the origo (shifted by $-P_1$ before rotation and $+P_1$ after), and the matrix multiplication gives the rotated vector. –  Berci Sep 30 '12 at 9:22