Question

If P(2, 4), Q(0, 3), R(3, 6) and S(5, y) are the vertices of a parallelogram PQRS, then the value of y is

(a) 7 (b) 5 (c) −7 (d) −8 [CBSE 2014]

Answer 1

It is given that P(2, 4), Q(0, 3), R(3, 6) and S(5, y) are the vertices of a parallelogram PQRS.



Join PR and QS, intersecting each other at O.

We know that the diagonals of the parallelogram bisect each other. So, O is the mid-point of PR and QS.

Coordinates of mid-point of PR = $\left(\frac{2+3}{2},\frac{4+6}{2}\right)=\left(\frac{5}{2},\frac{10}{2}\right)=\left(\frac{5}{2},5\right)$

Coordinates of mid-point of QS = $\left(\frac{0+5}{2},\frac{3+y}{2}\right)=\left(\frac{5}{2},\frac{3+y}{2}\right)$

Now, these points coincides at the point O.

$$\begin{gathered} \therefore \left(\frac{5}{2},\frac{3+y}{2}\right)=\left(\frac{5}{2},5\right) \\ \Rightarrow \frac{3+y}{2}=5 \\ \Rightarrow 3+y=10 \\ \Rightarrow y=7 \end{gathered}$$

Thus, the value of y is 7.

Hence, the correct answer is option A.