Question

If 2 and 3 are intercepts of a line \( L = 0 \), then the distance of \( L \equiv 0 \) from the origin is

• A. \( \frac{5}{\sqrt{13}} \)
• B. \( \frac{\sqrt{13}}{6} \)
• C. \( \frac{6}{\sqrt{13}} \)
• D. \( 1 \)

Hint:

Use intercept form \( \frac{x}{a} + \frac{y}{b} = 1 \) when x- and y-intercepts are given.

Answer 1

The Correct Option is C

Given intercepts on axes: x-intercept = 2, y-intercept = 3
Equation of line using intercept form: \( \frac{x}{2} + \frac{y}{3} = 1 \Rightarrow 3x + 2y - 6 = 0 \)
Use point to line distance from origin (0,0):
\[ D = \frac{|3(0) + 2(0) - 6|}{\sqrt{3^2 + 2^2}} = \frac{6}{\sqrt{9 + 4}} = \frac{6}{\sqrt{13}} \]