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.