Question

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 ______.

Options

• (–2, – 1)

• (–2, –3)

• (2, –1)

• (1, 2)

Answer 1

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 (2, –1).

Explanation:

Since PQRS is a parallelogram

It's Diagonals bisect each other

Therefore, Midpoint of PR = Midpoint of QS

`((3 + (-3))/2, (4 + (-2))/2) = ((-2 + x)/2, (3 + y)/2)`

`(0, 2/2) = ((-2 + x)/2, (3 + y)/2)`

Comparing x-coordinate

0 = `(-2 + x)/2`

0 = –2 + x

x = 2

Comparing y-coordinate

`2/2 = (3 + y)/2`

2 = 3 + y

y = –1

∴ Coordinates of point S is (2, –1)