Question

The three vertices of a parallelogram taken in order are $(-1,0),(3,1)$ and $(2,2)$ respectively. The coordinate of the fourth vertex is

• A. (2,1)
• B. (-2,1)
• C. (1,2)
• D. (1,-2)

Answer 1

Answer: (B)

Let $A(-1,0),B(3,1),C(2,2)$ and $D(x,y)$ be the vertices of a parallelogram ABCD taken in order. Since, the diagonals of a parallelogram bisect each other.
$\therefore$ Coordinates of the mid point of AC
= Coordinates of the mid-point of $BD$
$\Rightarrow \left(\frac{-1+2}{2},\frac{0+2}{2}\right)=\left(\frac{3+x}{2},\frac{1+y}{2}\right)$
$\Rightarrow \left(\frac{1}{2},1\right)=\left(\frac{3+x}{2},\frac{y+1}{2}\right)$
$\Rightarrow \frac{3+x}{2}=\frac{1}{2}$ and $\frac{y+1}{2}=1$
$\Rightarrow x=-2$ and $y=1$.
Hence the fourth vertex of the parallelogram is $(-2,1)$