Question

The points $(3,-4)$ and $(-6,2)$ are the extremities of a diagonal of a parallelogram. If the third vertex is $(-1,-3)$. Find the coordinates of the fourth vertex.

Answer 1

Let the fourth vertex be $(x,y)$

The two diagonals of a parallelogram bisect each other.

So, mid-point of $PR=$ Mid-point of $QS$

$(\frac{3-6}{2},\frac{-4+2}{2})=(\frac{x-1}{2},\frac{y-3}{2})$

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

Comparing,

$\frac{x-1}{2}=\frac{-3}{2}$

$x=-2$

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

$y=1$

$\therefore (x,y)=(-2,1)$