Question

If p is the length of the perpendicular from the origin to the line, whose intercepts with the coordinate axes are $\frac{1}{3}$ and $\frac{1}{4}$, then the value of $p$ is

• A. $\frac{3}{4}$
• B. $\frac{1}{12}$
• C. $5$
• D. $12$
• E. $\frac{1}{5}$

Answer 1

The correct option is E $\frac{1}{5}$

The line passes through $(\frac{1}{3},0)$ and $(0,\frac{1}{4})$.

Slope of the line $=\frac{\frac{1}{4}-0}{0-\frac{1}{3}}=-\frac{3}{4}$ and y-intercept is $\frac{1}{4}$

Therefore, equation of the line is $y=\frac{3}{4}x+\frac{1}{4}\text{or}3x-4y+1=0$.

Length of the perpendicular on the line from origin, $p=\frac{3\times 0-4\times 0+1}{\sqrt{3^2+4^2}}=\frac{1}{5}$.