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](/geometry-of-equations/r6366/images/p1.png)
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?