If p is the length of the perpendicular from the origin to the line, whose intercepts with the coordinate axes are `1/3` and `1/4`, then the value of p is :

Options

A. `3/4`
B. `1/12`
C. 5
D. `1/5`

Answer

D

Explanation

Equation of line in intercept form is ` x/a +y/b=1`
Here, a=1/3 and b=1/4
` x/(1//3) + y/(1//4) =1`
` Rightarrow 3x+4y-1=0`
Now perpendicular distance from (0,0) to the line is m
`(|3(0)+4(0)-1|)/(sqrt(3^(2)+4^(2))=p`
`1/sqrt(9+16) = p Rightarrow P=1/5`