If $A(2,-1)$ and $B(6,5)$ are two points the ratio in which the foot of the perpendicular from $(4,1)$ to $A B$ divides it, is

• A

  $8: 15$
• Correct answer
  B

  $5: 8$
• C

  $-5: 8$
• D

  $-8: 5$

Solution

Let $P(4,1)$ and $P D \perp A B$. Equation of $P D$ is $2 x+3 y-11=0$
$\therefore D$ divides $A B$ in the ratio $\begin{aligned} & \frac{-(2 \times 2+3 \times-1-11)}{2 \times 6+3 \times 5-11} \\ &= \frac{10}{16} \\ &= 5: 8\end{aligned}$

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