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Question

# A straight line through the origin O meets the parallel lines 4x+2y = 9 and 2x+y+ 6 = 0 at points P and Q respectively. Then the point O divides the segment PQ in ratio

A
1:2
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B
3:4
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C
2:1
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D
4:3
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Solution

## The correct option is B 3:4The given lines are 2x+y=9/2 (1) and 2x+y=−6 (2) Sings of constants on R.H.S. show that two lines lie on opp. sides of origin. Let any line through origin meets these lines in P and Q respectively then req. ratio is OP: OQ Now inΔOPAandΔOQC, ∠POA=≤QOC(ver.opp.∠′s) ∠PAO=≤OCQ(alt.int.∠′s) ∴ΔOPA ~ΔOQC (by AAA similarity) ∴OPOQ=OAOC=9/43=34 ∴ Req.ratio is 3:4.

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