Coordinate Geometry: JEE Main 2026 Mathematics 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 $\left(\frac{1}{2}, -5\right)$ from the line L is equal to :