Question

The diagram shows a parallelogram DEFG.
the point M is the midpoint of the diagonals DF and EG.
calculate .
a) the coordinate of M
b) the coordinate of the vertex D.

Answer 1

Given :

$M$ is the mid point of $EG$

$\therefore$ Co-ordinates of M are $(\frac{-3-7}{2},\frac{-2+3}{2})$ [by section formula]

$M=(-5,\frac{1}{2})$

Now again $M$ is the mid point of $DF$ and $\frac{DM}{MF}=1$

Let $D=(x,y)$

$(\frac{x-1}{2},\frac{y+3}{2})=(-5,\frac{1}{2})$

Comparing we get

$\frac{x-1}{2}=-5$

$\Rightarrow x=-9$

$\frac{y+3}{2}=\frac{1}{2}$

$y=-2$

$\therefore$ co-ordinater of $D$ is $(-9,-2)$