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 :

• A. \( 2\sqrt{5} \)
• B. \( 2\sqrt{10} \)
• C. \( 3\sqrt{10} \)
• D. \( \sqrt{10} \)

Hint:

Any line passing through the center of a rectangle, parallelogram, or circle bisects its area.

Answer 1

The Correct Option is B