Question

If P(1, 2), Q(4, 6), R(5, 7) and S(a, b) are the vertices of a parallelogram PQRS then

(a) a = 2, b = 4

(b) a = 3, b = 4

(c) a = 2, b = 3

(d) a = 2, b = 5

Answer 1

The correct option (c) a = 2, b = 3

Explanation:

P(1, 2), Q(4, 6), R(5, 7), S(a, b)

diagonals bisect each other, hence

[{(1 + 5)/2}, {(7 + 2)/2}] = [{(a + 4)/2}, {(b + 6)/2}]

∴ a + 4 = 6   and     b + 6 = 9

∴ a = 2    and     b = 3