PQ and RS&nbs...
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
3
4
1
2
Correct answer is D
Gradient PQ, P(1,q) and Q(3,2)
=(2−q)(3−1)=(2−q)2
Gradient of RS : R(3,4) and S(5,2q)
=(2q−4)(5−3)=(2q−4)2=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
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