Given a right angle and the equations of two sides, can we find the third?

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In the triangle \(ABC\) the equations of two of the sides are \(2y=x+2\) and \(y=2x-2\). Given that \(A\) is the point \((4,3)\) and that \(A\hat{B}C\) is \(90^\circ\), find the equation of the third side.

How could we find out which of those sides goes through \(A\)?