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AP EAMCET · Maths · Straight Lines

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

  1. A \(1: 2\)
  2. B \(2: 1\)
  3. C \(3: 4\)
  4. D \(4: 3\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(3: 4\)

Step-by-step Solution

Detailed explanation

Rewrite the lines as: \( L_1: 4x+2y-9=0 \) and \( L_2: 4x+2y+12=0 \). The ratio in which the origin \(O\) divides the line segment \(PQ\) is the ratio of the perpendicular distances from \(O\) to \(L_1\) and \(L_2\). Ratio \( = \frac{|-9|}{|12|} = \frac{9}{12} = \frac{3}{4} \).