11. Five marks exercise problems V

The points $A(-3, 6)$, $B(0, 7)$ and $C(1, 9)$ are the mid-points of the sides $DE$, $EF$ and $FD$ of a triangle $DEF$. Show that the quadrilateral $ABCD$ is a parallelogram.

 

Proof:

 

The vertices of $D$ $=$ $\left(i,i\right)$

 

Mid-point of $AC$ $=$ $\left(i,\frac{i}{i}\right)$

 

Mid-point of $BD$ $=$ $\left(i,\frac{i}{i}\right)$

 

 

$ABCD$ is a parallelogram.