Question

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

• A. $\left(\frac{81}{25},\frac{92}{25}\right)$
• B. $\left(\frac{92}{25},\frac{81}{25}\right)$
• C. $\left(\frac{46}{26},\frac{54}{24}\right)$
• D. $\left(-\frac{81}{25},-\frac{92}{25}\right)$

Answer 1

The correct option is A $\left(\frac{81}{25},\frac{92}{25}\right)$

If the foot of perpendicular is $(a,b)$, then $3a-4b+5=0$..(1)

Now equation of line passing through the point $(3,4)$ and perpendicular to given line is,

$y-4=-\frac{4}{3}(x-3)\Rightarrow 4x+3y-24=0$

Also the point $(a,b)$ will satisfy above line

$4a+3b-24=0$.......(2)

Now solving (1) and (2) we get $a=\frac{81}{25},b=\frac{92}{25}$