Question

If $A(-2,1),B(1,0),C(x,3)$ and $D(1,y)$ are the vertices of parallelogram, then find the values of $x$ and $y$.

Answer 1

We know that, in parallelogram diagonals are bisect each other.

$\therefore$ Mid-point of $AC=$ Mid-point of $BD$

$\Rightarrow$ $(\frac{-2+x}{2},\frac{1+3}{2})=(\frac{1+1}{2},\frac{0+y}{2})$

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

Now, $\frac{-2+x}{2}=1$

$\Rightarrow$ $-2+x=2$

$\therefore$ $x=4$

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

$\therefore$ $y=4$

Hence, the values of $x$ and $y$ are $4$ and $4$.