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

Options

• 7

• 5

• -7

• -8

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.

\[\therefore \left( \frac{5}{2}, \frac{3 + y}{2} \right) = \left( \frac{5}{2}, 5 \right)\]

\[ \Rightarrow \frac{3 + y}{2} = 5\]

\[ \Rightarrow 3 + y = 10\]

\[ \Rightarrow y = 7\]

Thus, the value of y is 7.