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COMEDK202510 May 2025Morning ShiftMathematicsStraight LinesActual

Distance of the point (-2,3) from the line 12 x-5 y-2=0 is 41 k . Then the value of k is

Options

  1. A134
  2. B13
  3. C1
  4. D13

Correct answer

D. 13

Step-by-step solution

The distance d of a point (x₁, y₁) from the line Ax + By + C = 0 is given by the formula d = |Ax₁ + By₁ + C| A^2 + B^2 . Given the point (-2, 3) and the line 12x - 5y - 2 = 0 , we have A = 12 , B = -5 , C = -2 , x₁ = -2 , and y₁ = 3 . Substituting these values into the formula: d = |12(-2) - 5(3) - 2| 12^2 + (-5)^2 d = |-24 - 15 - 2| 144 + 25 d = |-41| 169 d = 41 13 Comparing this with the given distance 41 k , we find k = 13 . Answer: 13

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