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.

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

Ref: R5661

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.