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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 the ratio


Your Answer
A
1:2
Correct Answer
B
3:4
Your Answer
C
2:1
Your Answer
D
4:3

Solution

The correct option is B 3:4
The given lines are 
2x+y=9/2             (1)
and 2x+y=6             (2)
Signs 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 the required 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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