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

विकल्प

• 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 = $$(\frac{2+3}{2},\frac{4+6}{2})=(\frac{5}{2},\frac{10}{2})=(\frac{5}{2},5)$$

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

Now, these points coincides at the point O.

$$\therefore (\frac{5}{2},\frac{3+y}{2})=(\frac{5}{2},5)$$

$$\Rightarrow \frac{3+y}{2}=5$$

$$\Rightarrow 3+y=10$$

$$\Rightarrow y=7$$

Thus, the value of y is 7.