Question

The foot of the perpendicular from $(a,0)$ on the line $y=mx+\frac{a}{m}$ is:

• A. $(0,-\frac{1}{2})$
• B. $(0,\frac{a}{m})$
• C. $(0,-\frac{a}{m})$
• D. $(0,0)$

Answer 1

The correct option is B $(0,\frac{a}{m})$

$y-mx-\frac{a}{m}=0$

$\frac{x-a}{-m}=\frac{y-0}{1}=\frac{-(-ma-\frac{a}{m})}{1+m^2}=\frac{a}{m}$

$x=a-a$ and $y=\frac{a}{m},$

$x=0$

$(x,y)=(0,\frac{a}{m})$ is a foot of the perpendicular from $(a,0)$ on line $y=mx+\frac{a}{m}.$