Question

If the point $(x,-1),(3,y),(-2,3)$ and $(-3,-2)$ be the vertices of a parallelogram, then?

• A. $x=2,y=4$
• B. $x=1,y=2$
• C. $x=4,y=2$
• D. None of these

Answer 1

The correct option is A $x=2,y=4$

The points $A(x,-1),B(3,y),C(-2,3),D(-3,-2)$ are the vertices of a parallelogram..

We know that diagonals of a parallelogram bisect each other.

Let O be the point of bisection.

$AO=OC$ and $BO=OD$

O is the midpoint of $AC$ as well as $BD$.

Considering $AC$, $O(\frac{x-2}{2},\frac{-1+3}{2})$

Considering $BD$, $O(\frac{3-3}{2},\frac{y-2}{2})$

Equating the coordinates,

$\frac{x-2}{2}=0$

$x=2$

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

$y=4$

Option $\text{A}$ is the correct answer