Question

If $(4,3)$ and $(-2,-1)$ are positive vertex of a parallelogram and third vertex $(1,0)$ then the product of co-ordinates of the four vertex?

Answer 1

We know that diagonals of a parallelogram bisect each other.

Let the point of intersection of diagonals be $P(m,n)$

Co-ordinates of three vertex of parallelogram are $(4,3),(1,0)$ and $(-2,-1)$

$\therefore m=\frac{(-2+4)}{2}=1$

Also, $n=\frac{(-1+3)}{2}=1$

Let the fourth vertex of a parallelogram be $(x,y)$

$\Rightarrow m=\frac{(1+x)}{2}$

$\Rightarrow 1=\frac{(1+x)}{2}$

$\Rightarrow x=1$

Also, $n=\frac{(0+y)}{2}$

$\Rightarrow 1=\frac{(0+y)}{2}$

$\Rightarrow y=2$

Product of co-ordinates $=1\times 2=2$