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

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?

  1. the coordinates of \(C\),

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

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

How do we calculate the area of a rectangle?