In the rectangle \(ABCD\), \(A\) and \(B\) are the points \((4,2)\) and \((2,8)\) respectively.
![Graph with the rectangle ABCD. A and B are on the left-facing side of the rectangle, C is the top-right vertex, and D is the bottom-right](/geometry-of-equations/r6366/images/p1.png)
Given that the equation \(AC\) is \(y=x-2\), find
the equation of \(BC\),
the coordinates of \(C\),
the coordinates of \(D\),
the area of the rectangle \(ABCD\).
This question needs an exact method that goes beyond accurate drawing.