Can we find a rectangle from two vertices and a diagonal?

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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 \(D\).

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