Straight Lines
Line Bisecting Rectangle Area — Distance from Point
nta_pyq_2026_jan
Grade None
Question:
A rectangle is formed by the lines $x=0,y=0,x=3$ and $y=4$. Let the line $L$ be perpendicular to $3x+y+6=0$ and divide the area of the rectangle into two equal parts. Then the distance of the point $\left(\dfrac{1}{2},-5\right)$ from the line $L$ is equal to:
$\sqrt{10}$
$2\sqrt{5}$
$2\sqrt{10}$
$3\sqrt{10}$
Step-by-Step Solution
Key Concept: Center of rectangle $=(3/2,2)$. $L\perp3x+y+6=0$ means slope of $L=1/3$. Any line through the center bisects area. $L$: $y-2=\tfrac{1}{3}(x-3/2)\Rightarrow2x-6y+9=0$.
Distance $=2\sqrt{10}$.
Correct Answer: 3