parallelogram and using determinants find tha area

Question

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.

Answer 1

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.

$$\text{Area of }ABDC = \left| \vec{AB} \times \vec{AC} \right|$$