Question

Four vertices of a parallelogram taken in order are $(-3,-1),(a,b),(3,3)$ and $(4,3).$ What will be the ratio of a and b ?

• A. $4:1$
• B. $1:2$
• C. $1:3$
• D. $3:1$

Answer 1

The correct option is A $4:1$

Given four vertices pf parallelogram

A(-3,-1) ,B(a,b) ,C(3,3) and D(4,3)

Area $=\frac{1}{2}|(x_1{y}_2-y_1{x}_2)+(x_3{y}_4-x_4{y}_3)+...+(x_n{y}_1-y_n{x}_1)|=\frac{1}{2}\left|\right(-3b+a)+(3a-3b)+(9-12)+(-4+9\left)\right|\frac{1}{2}\left|\right(-3b+a)+3a-3b-3+5|=\Rightarrow 2a-3b+1=0$

Coordinate of mid points of diagonal $BD=(\frac{a+4}{2},\frac{b+3}{2})$

$AC=(\frac{-3+3}{2},\frac{-1+3}{2})=(0,1)\frac{a+4}{2}=0,\frac{b+3}{2}=1a=-4,b=-1$

$\therefore$ ratio of $\frac{a}{b}=\frac{-4}{-1}=4:1$