Question 14

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Jambmaths question: 

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

Option A: 

4

Option B: 

1

Option C: 

2

Option D: 

3

Jamb Maths Solution: 

$\begin{align}  & \text{For two lines to be parallel},\text{ the slopes must be equal }{{m}_{\text{1}}}={{m}_{\text{2}}} \\ & m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} \\ & {{l}_{1}}:P(\underbrace{1,q}_{{{x}_{1}}:{{y}_{1}}}):Q(\underbrace{3,2}_{{{x}_{2}},{{y}_{2}}}) \\ & {{m}_{1}}=\frac{2-q}{3-1}=\frac{2-q}{2}---(i) \\ & {{l}_{2}}:R(\underbrace{3,4}_{{{x}_{1}},{{y}_{1}}}):S(\underbrace{5,2q}_{{{x}_{2}},{{y}_{2}}}) \\ & {{m}_{2}}=\frac{2q-4}{5-3}=\frac{2q-4}{2}-----(ii) \\ & \text{For parallel lines} \\ & {{m}_{1}}={{m}_{2}} \\ & \frac{2-q}{2}=\frac{2q-4}{2} \\ & 2-q=2q-4 \\ & 3q=6 \\ & q=2 \\\end{align}$

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