Question

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

• 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)