Can we show we have three corners of a rectangle?

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The coordinates of the points \(A\), \(B\), \(C\) are \((-2,1)\), \((2,7)\), \((5,5)\) respectively. Prove that these points form three corners of a rectangle and that \(AB=2BC\).

If \(D\) is the fourth corner of the rectangle, calculate the distance of \(C\) from the diagonal \(BD\).