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

Given that the equation \(AC\) is \(y=x-2\), find

  1. the equation of \(BC\),

  2. the coordinates of \(C\),

  3. the coordinates of \(D\),

  4. the area of the rectangle \(ABCD\).

This question needs an exact method that goes beyond accurate drawing.