Mathematics · Straight lines

JEE Main 2026 — 23 January, Morning Shift — Question 4

A rectangle is formed by the lines $x=0, y=0$ , $\mathrm{x}=3$ and $\mathrm{y}=4$ . 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 $\left(\frac{1}{2},-5\right)$ from the line L is equal to :

Option A:
$2 \sqrt{5}$
Option B:
$3 \sqrt{10}$
Option C:
$\sqrt{10}$
Option D:
$2 \sqrt{10}$
Correct

Answer: D

Step-by-step solution

Line is $\mathrm{y}=\frac{\mathrm{x}}{3}+\mathrm{C}$

Line passes through $\left(\frac{3}{2}, 2\right)$

$2=\frac{1}{2}+\mathrm{C} \Rightarrow \mathrm{C}=\frac{3}{2}$

$\mathrm{y}=\frac{\mathrm{x}}{3}+\frac{3}{2}$

$\Rightarrow 6 \mathrm{y}=2 \mathrm{x}+9$ Line is $2 x-6 y+9=0$

& Dist $=\left|\frac{1+30+9}{\sqrt{40}}\right|=\sqrt{40}=2 \sqrt{10}$

Answer key and solution verified before publishing.

Practise Straight lines

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.

Solve a similar one free

Exam: JEE Main 2026
Paper: 23 January, Morning Shift
Subject: Mathematics
Chapter: Straight lines
Topic: Angle between lines, perpendicular distance & distance between parallel lines, foot, image

The vertices B and C of a triangle ABC lie on the line x/1=1-y/-2=z-2/3 . The coordinates of A and B are (1,6,3) and (4,9, alpha)…

Answer: D

Step-by-step solution

Practise Straight lines

More Straight lines questions from this paper