Question

If A $(-2,-1)$, B$(a,0)$, C$(4,b)$ and D $(1,1)$ are the vertices of a parallelogram, then the values of $a$ and $b$ respectively are

• A. $3,1$
• B. $-3,1$
• C. $1,3$
• D. $-1,-3$

Answer 1

The correct option is C $1,3$

The diagonals of a parallelogram bisect each other, therefore co-ordinates of mid-points of both the diagonals are the same co-ordinates of mid-point of diagonal AC
$=(\frac{4-2}{2},\frac{b-1}{2})=(1,\frac{b-1}{2})$
Co-ordinate of mid-point of diagonal BD
$=(\frac{1+a}{2},\frac{2-0}{2})=(\frac{1+a,}{2},1)\Rightarrow \frac{1+a}{2}=1$and$\frac{b-1}{2}=1\Rightarrow 1+a=2$and$b-1=2\Rightarrow a=+1$and$b=3$