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JEE Main 202623 JanuaryMorning Shift
Exam
JEE Main
Year
2026
Date
23 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2026 · 23 January · Morning Shift · Mathematics · Straight Lines

A rectangle is formed by the lines x=0, y=0, x=3 and y=4 . Let the...

A rectangle is formed by the lines x=0,y=0,x=3andy=4x=0, y=0, x=3 and y=4. Let the line L be perpendicular to 3x+y+6=03 x+y+6=0 and divide the area of the rectangle into two equal parts. Then the distance of the point (12,−5)\left(\frac{1}{2},-5\right) from the line LL is equal to :

Options

  1. A10\sqrt{10}
  2. B252 \sqrt{5}
  3. C2102 \sqrt{10}
  4. D3103 \sqrt{10}

Correct answer

C. 2102 \sqrt{10}

Step-by-step solution

Rectangle: x=0,y=0,x=3,y=4x=0, y=0, x=3, y=4, area =12= 12. Center =(3/2,2)= (3/2, 2).
Slope of 3x+y+6=03x+y+6=0 is −3-3, so slope of L=1/3L = 1/3.
A line through the center of a rectangle bisects its area. So LL passes through (3/2,2)(3/2, 2) with slope 1/31/3:
y−2=13(x−3/2)y - 2 = \frac{1}{3}(x - 3/2)
⇒x−3y+92=0\Rightarrow x - 3y + \frac{9}{2} = 0
⇒2x−6y+9=0\Rightarrow 2x - 6y + 9 = 0.
Distance from (1/2,−5)(1/2, -5):
d=∣2(1/2)−6(−5)+9∣4+36d = \frac{|2(1/2) - 6(-5) + 9|}{\sqrt{4+36}}
=∣1+30+9∣40=40210=210= \frac{|1+30+9|}{\sqrt{40}} = \frac{40}{2\sqrt{10}} = 2\sqrt{10}.
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