Can we show this parallelogram is a rectangle?

Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

The diagram shows a parallelogram \(ABCD\) with \(A\) and \(C\) on the coordinate axes. The equation of \(AB\) is \(y=2x+1\) and the equation of \(BC\) is \(2y+x=12\).

1. Show that \(ABCD\) is a rectangle.
2. Find the coordinates of \(A\), \(B\), \(C\) and \(D\).
3. Find the area of \(ABCD\).