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Manipal MET2015MathematicsStraight Lines

The distance of the point (1,1) from the line 2 x-3 y-4=0 in the direction of the line x+y=1 , is

Options

  1. A2
  2. B5 2
  3. C1 2
  4. D1 2

Correct answer

A. 2

Step-by-step solution

The equation of a line through P(1,1) and parallel to x+y=1 , is x-1 3 4 = y-1 3 4 Let P M=r . Then, the coordinates of M given by x-1 3 4 = y-1 3 4 =r is (1- r 2 , 1+ r 2 ) M lies on 2 x-3 y-4=0 . 2 (1- r 2 )-3 (1+ r 2 )-4=0 array rlrl & 2- 2 r 2 -3- 3 r 2 -4 & =0 & -5- 5 r 2 & =0 & & r & =- 2 array Hence, P M= 2

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