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JEE Main202623 January 2026Morning ShiftMathematicsStraight LinesActual

A rectangle is formed by the lines x=0, y=0, x=3 and y=4 . Let the line L be perpendicular to 3 x+y+6=0 and divide the area of the rectangle into two equal parts. Then the distance of the point ( 1 2 ,-5 ) from the line L is equal to :

Options

  1. A10
  2. B2 5
  3. C2 10
  4. D3 10

Correct answer

C. 2 10

Step-by-step solution

Rectangle: x=0, y=0, x=3, y=4 , area = 12 . Center = (3/2, 2) . Slope of 3x+y+6=0 is -3 , so slope of L = 1/3 . A line through the center of a rectangle bisects its area. So L passes through (3/2, 2) with slope 1/3 : y - 2 = 1 3 (x - 3/2) x - 3y + 9 2 = 0 2x - 6y + 9 = 0 . Distance from (1/2, -5) : d = |2(1/2) - 6(-5) + 9| 4+36 = |1+30+9| 40 = 40 2 10 = 2 10 .

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