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COMEDK2021MathematicsStraight Lines

If 3 and 4 are intercepts of a line L 0 , then the distance of L 0 from the origin is

Options

  1. A5 units
  2. B12 units
  3. C5 12 unit
  4. D12 5 units

Correct answer

D. 12 5 units

Step-by-step solution

The intercept form of a line with x-intercept a and y-intercept b is given by x a + y b = 1 . Given a = 3 and b = 4 , the equation of the line L is x 3 + y 4 = 1 . Multiplying by 12, we get 4x + 3y = 12 , or 4x + 3y - 12 = 0 . The distance d of a line Ax + By + C = 0 from the origin (0, 0) is given by d = |C| A^2 + B^2 . Substituting A = 4 , B = 3 , and C = -12 , we get d = |-12| 4^2 + 3^2 = 12 16 + 9 = 12 25 = 12 5 . Answer: 12 5 units

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