Different Rectangles
Can you draw two different rectangles, whose diagonal is represented by the same vector?
Age
14 to 16
Challenge level
Problem
Draw two different rectangles (with different areas), with vertices at whole number co-ordinates, whose diagonal is represented by the vector $\begin{pmatrix}3\\4\end{pmatrix}$
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
The most obvious rectangle is that with vertices at $(0,0)$, $(3,0)$, $(3,4)$ and $(0,4)$.
The second has vertices at $(0,0)$, $(4,2)$, $(3,4)$ and $(-1,2)$.