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
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
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
Source: Myschool Past Questions Archive (Record #8835)