Question

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

Answer 1

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

$\Rightarrow$ $(\frac{-1+2}{2},\frac{0+2}{2})$ = $(\frac{3+x}{2},\frac{1+y}{2})$

$\Rightarrow$ $(\frac{1}{2},1)$ = $(\frac{3+x}{2},\frac{y+1}{2})$

$\Rightarrow$ $\frac{3+x}{2}=\frac{1}{2}and\frac{y+1}{2}=1$

$\Rightarrow$ x = -2 and y = 1

Hence, the fourth vertex of the parallelogram is (-2, 1).