Coordinates rotation by $120$ degree If I have a point on a standard grid with coordinates say:  

$A_1=(1000,0)$
  $A_2=(707,707)$  

Is there a easy way to transfer this points to $\pm 120$ degrees from the origin $(0,0)$, and keeping the same distance?
So for $A_1$, the result should be something like: 
$B_1=(800,-200);\  C_1=(800,-200)$
I can make this with triangles and calculate it but there should be some formula. I need a formula to use with software.

In general, the rotation matrix of angle $\theta$ is $$r_\theta=\left(\begin{array}{cc}\cos\theta & -\sin\theta\\ \sin\theta & \cos\theta\end{array}\right).$$
In your case, $\theta=\pm120°$, so $\cos\theta=-1/2$ and $\sin\theta=\pm\frac{\sqrt 3}2$.
You just have to apply the matrix to the vector to get the image of the vector by the rotation.
