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. - Mathematics

Sum

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.

Solution

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.

∴ Coordiantes 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}\text{ and }\frac{y+1}{2}=1

⇒ x = – 2 and y = 1

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

Concept: Section Formula
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