Can we find the coordinates of this tilted rectangle?

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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

1. the equation of \(BC\),

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

2. the coordinates of \(C\),

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

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

How do we calculate the area of a rectangle?