# parallelogram and using determinants find tha area [closed]

Show that the point $A(0,0)$, $B(2,5)$, $C(7,-3)$, $D(9,2)$ are vertices of the parallelogram and using determinants to find its area.

## closed as off-topic by JonMark Perry, Claude Leibovici, mrp, Namaste, TheGeekGreekFeb 8 '17 at 14:08

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• If you plot the points on a Cartesian plane and find the slope of the opposite sides to be equal, meaning that the lines are parallel, then you can prove it is a parallelogram. – Harnoor Lal Feb 8 '17 at 9:03
• Then create a matrix whose columns are vectors representing the two non-parallel sides and compute its determinant. – SquirtleSquad Feb 8 '17 at 9:23

Note that $A$, $B$, $C$, $D$ are not in correct order.
Since $A+D=B+C=(9,2)$, $AD$ and $BC$ bisect each other.
Hence, $ABDC$ is a parallelogram.
$$\text{Area of }ABDC = \left| \vec{AB} \times \vec{AC} \right|$$