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Manipal MET2021MathematicsStraight Lines

The ratio in which the segment joining (2,1) and (0,-2) is divided by the line 2 x-3 y+4=0 is

Options

  1. A1: 2
  2. B2: 1
  3. C-1: 2
  4. D-2: 1

Correct answer

C. -1: 2

Step-by-step solution

Suppose the segment 2 x-3 y+4=0 divides line segment joining A(2,1) and B(0,-2) in the ratio k: 1 at point C . C is ( 2 k+1 , -2 k+1 k+1 ) Since, C lies on 2 x-3 y+4=0 array lr & 4 k+1 -3 (-2 k+1) k+1 +4=0 & 4+6 k-3+4 k+4=0 & 10 k+5=0 & k=- 1 2 & Ratio is -1: 2 . array

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