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Manipal MET2014MathematicsStraight Lines

The distance of the point (3,5) from 2 x+3 y-14=0 measured parallel to x-2 y=1 is

Options

  1. A7 5
  2. B7 13
  3. C5
  4. D13

Correct answer

C. 5

Step-by-step solution

Let the equation of the line parallel to x-2 y=1 is x-2 y+ =0 Since, it passes through (3,5) 3-10+ =0 =7 The line is x-2 y+7=0 . The point of intersection of x-2 y+7=0 and 2 x+3 y-14=0 is (1,4) . The distance between (3,5) and (1,4)= (3-1)^2+(5-4)^2 = 4+1 = 5

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