Question

The co-ordinates of foot of the perpendicular drawn on line $3x-4y-5=0$ from the point $(0,5)$ is

• A. $(1,3)$
• B. $(2,3)$
• C. $(3,2)$
• D. $(3,1)$

Answer 1

The correct option is D $(3,1)$

Let coordinate of foot of perpendicular be $(h,k)$, then

$\frac{h-A_1}{A_1}=\frac{k-B_1}{B_1}=-\frac{A_1\times h+B_1\times k+C_1}{{A_1}^2+{B_1}^2}$

$\frac{h-0}{3}=\frac{k-5}{-4}=-\frac{3\times 0-4\times 5-5}{3^2+4^2}$

$\Rightarrow \frac{h}{3}=\frac{k-5}{-4}=1$
$\Rightarrow h=3,k=1$