Interactive diagram

The points \(A(1,2)\) and \(B(-2,1)\) are two vertices of a rectangle \(ABCD\). The diagonal \(CA\) produced passes through the point \((2,9)\). Calculate the coordinates of the vertices \(C\) and \(D\).

In this applet, \(A\) and \(B\) are fixed. You can move \(C\).