Question

If $(-1,2),(2,-1)$ and $(3,1)$ are any three vertices of a parallelogram then the fourth vertex $(a,b)$ will be such that

• A. $a=2,b=0$
• B. $a=-2,b=0$
• C. $a=-2,b=6$
• D. $a=0,b=4$

Answer 1

The correct option is D $a=0,b=4$

REF.Image

Diagonal of ||gm bisect each

other

so midpoint of BD is same

as midpoint of AC.

Midpoint of AC = $(\frac{-1+3}{2},\frac{2+1}{2})=(1,\frac{3}{2})$ from section formula

Midpoint of BD = $(\frac{a+2}{2},\frac{b-1}{2})$

so $\frac{a+2}{2}=1\Rightarrow a=0$

$\frac{b-1}{2}=\frac{3}{2}\Rightarrow b=4$