Mathematics

PQ and RS are two parallel lines. If the coordinates of P, Q, R, S…

PQ and RS are two parallel lines. If the coordinates of P, Q, R, S are (1,q), (3,2), (3,4), (5,2q) respectively, find the value of q

  • A.
    3
  • B.
    4
  • C.
    1
  • D.
    2
Correct Answer: Option D
Explanation

Gradient PQ, P(1,q) and Q(3,2)
(=frac{(2-q)}{(3-1)} = frac{(2-q)}{2})
Gradient of RS : R(3,4) and S(5,2q)
(= frac{(2q-4)}{(5-3)}= frac{(2q-4)}{2} = frac{2(q-2)}{2})
= q-2
Since PQ and RS are parallel,
their gradients are equal
(∴ frac{(2-q)}{2} = q-2)
2-q = 2(q-2)
2-q = 2q-4
2+4 = 2q+q
6 = 3q
q = 2