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

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

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

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

$\Rightarrow x=-2andy=1$
Hence, the fourth vertex of the parallelogram is (-2, 1)