Question

If $(1,2),(4,y),(x,6)$ and $(3,5)$ are the vertics of a parallelogram taken in order, find $x$ and $y$.

Answer 1

The vertices of a parallelogram is given as $A\left(1,2\right),B\left(4,y\right),C\left(x,6\right),D\left(3,5\right)$.

It is known that,

$\left(\frac{x_3+x_1}{2},\frac{y_3+y_1}{2}\right)=\left(\frac{x_4+x_2}{2},\frac{y_4+y_2}{2}\right)$

So,

$\left(\frac{x+1}{2},\frac{6+2}{2}\right)=\left(\frac{3+4}{2},\frac{5+y}{2}\right)$

$\left(\frac{x+1}{2},4\right)=\left(\frac{7}{2},\frac{5+y}{2}\right)$

Comparing both sides,

$\frac{x+1}{2}=\frac{7}{2}$

$x+1=7$

$x=6$

And,

$\frac{5+y}{2}=4$

$5+y=8$

$y=3$

Therefore,

$x=6,y=3$