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MHT CET202523 Apr 2025Morning ShiftMathematicsStraight LinesActual

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

Options

  1. A3 2 8 units
  2. B3 10 4 units
  3. C10 units
  4. D5 5 units

Correct answer

B. 3 10 4 units

Step-by-step solution

The given point is P = (1,2) , with distance measured from line L₁: x+y=0 parallel to line L₂: 3x-y=2 . The direction vector for L₂ is derived from its slope m=3 , giving the line through P parallel to L₂ as y - 2 = 3(x - 1) , simplifying to 3x - y - 1 = 0 . Intersecting this with L₁ by substituting y = -x yields 3x - (-x) - 1 = 0 , so 4x = 1 and x = 1 4 with y = - 1 4 . The distance between (1,2) and ( 1 4 , - 1 4 ) is found as ( -3 4 )^2 + ( -9 4 )^2 = 9 16 + 81 16 = 90 16 = 3 10 4 . Final answer: 3 10 4 units.

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