Question

If the points $A(-2,-1),B(1,0),C(a,3)$ and $D(1,b)$ form a parallelogram $ABCD$, find the value of $a$ and $b$.

Answer 1

In the parallelogram $ABCD$ , $AC$ and $BD$ are the diagonals.

Co-ordinates of mid-point of $AC=(\frac{-2+a}{2},\frac{1+1}{2})$

Co-ordinate of mid-point of $BD=(\frac{1+1}{2},\frac{0+b}{2})$

It is known that diagonals of the parallelogram bisect each other. Thus mid point of $AC$ and $BD$ coincide each other.

Thus,

$\frac{-2+a}{2}=1⟹a=4$

$\frac{1+1}{2}=\frac{b}{2}⟹b=2$