In the rectangle \(ABCD\), \(A\) and \(B\) are the points \((4,2)\) and \((2,8)\) respectively.

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.*