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COMEDK2022MathematicsStraight Lines

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

Options

  1. A125 3
  2. B125 3
  3. C5 5 3
  4. D5 3 3

Correct answer

C. 5 5 3

Step-by-step solution

The given point is P(1, 2) and the line is L: x + y + 2 = 0 . The line passing through P(1, 2) and parallel to 2x - y = 5 has a slope m = 2 . The equation of this line is y - 2 = 2(x - 1) , which simplifies to y = 2x or 2x - y = 0 . To find the intersection point Q of x + y + 2 = 0 and 2x - y = 0 , we substitute y = 2x into the first equation: x + 2x + 2 = 0 3x = -2 x = - 2 3 . Then y = 2(- 2 3 ) = - 4 3 . So, Q = (- 2 3 , - 4 3 ) . The distance PQ is given by the distance formula: PQ = (1 - (- 2 3 ))^2 + (2 - (- 4

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