2006

Mathematics

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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: 2

Explanation

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 generation are equal ∴((2-q))/2=q-2. 2-q = 2(q-2) 2-q = 2q-4 2+4 = 2q+q 6 = 3q q = 2

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 generation are equal ∴((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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