Question

If the three consecutive vertices of a parallelogram PQRS are P(–9, 1), Q(–15, –1) and R(15, –1), then the coordinates of S are

• A. (-9, 21)
• B. (-21, -1)
• C. (21, 1)
• D. (1, 21)

Answer 1

The correct option is C (21, 1)

Given that the three consecutive vertices of the parallelogram are P(–9, 1), Q(–15, –1) and R(15, –1).

Let the coordinates of the fourth vertex S be (a, b).



We know that the diagonals of a parallelogram bisect each other. Therefore, O is the mid-point of PR as well as QS.

Now, mid-point of PR $=(\frac{15-9}{2},\frac{-1+1}{2})=(3,0)$

Mid-point of QS $=(\frac{-15+a}{2},\frac{-1+b}{2})$

$\therefore \frac{-15+a}{2}=3and\frac{-1+b}{2}=0$

$\Rightarrow -15+a=6and-1+b=0$

$\Rightarrow a=6+15=21andb=1$

Thus, the coordinates of fourth vertex S are (21, 1).

Hence, the correct answer is option (c).