If the vertices of a parallelogram PQRS taken in order are P(3, 4), Q(-2, 3) and R(-3, -2), then the coordinates of its fourth vertex S are

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Solution

Q.
If the vertices of a parallelogram PQRS taken in order are P(3, 4), Q(-2, 3) and R(-3, -2), then the coordinates of its fourth vertex S are

1 (-2, -1)

2 (-2, -3)

3 (2, -1)

4 (1, 2)

Ans.
(3)

We know that the diagonals of a parallelogram bisect each other.

Therefore, midpoint of QS = midpoint of PR. Let the coordinate of S is (x, y)

$\Rightarrow (\frac{x - 2}{2}, \frac{y + 3}{2}) = (\frac{3 - 3}{2}, \frac{4 - 2}{2})$

$\Rightarrow \frac{x - 2}{2} = \frac{3 - 3}{2} and \frac{y + 3}{2} = \frac{4 - 2}{2}$

$\Rightarrow x - 2 = 0 \Rightarrow x = 2$

$and y + 3 = 2 \Rightarrow y = - 1$

Hence, fourth vertex S are (2, -1).

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