If the foot of the perpendicular drawn from the point $(0, k)$ to the line $3 x-4 y-5=0$ is $(3,1)$, then what is the value of $k$ ?

• A

  3
• B

  4
• Correct answer
  C

  5
• D

  6

Solution

Slope of the line, $3 x-4 y-5=0$ is $m=\frac{3}{4}$ Slope of any line perpendicular to $3 x-4 y-5=0$ is $m^{\prime}=-\frac{4}{3}$.
Now, required line passes through the points $(0, K)$ and $(3,1)$. $\therefore \frac{K-1}{0-3}=-\frac{4}{3} \Rightarrow K=5 \text {. }$

Hence, the correct answer is option: 'C'.