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

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

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

- the equation of \(BC\),

If we know that \(BC\) is perpendicular to \(AB\), what can we say about the gradients of these lines?

- the coordinates of \(C\),

We know the equations of \(BC\) and \(AC\) now…

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

How do we calculate the area of a rectangle?