A straight line cuts off an intercept of 2 units on the positive direction of $x$-axis and passes through the point $(-3,5)$. What is the foot of the perpendicular drawn from the point $(3,3)$ on this line?

• A

  $(1,3)$
• B

  $(2,0)$
• C

  $(0,2)$
• Correct answer
  D

  $(1,1)$

Solution

The given line passes through $(-3,5)$ and $(2,0)$. Its equation is
$\begin{aligned} & y-y_1=\left(\frac{y_2-y_1}{x_2-x_1}\right)\left(x-x_1\right) \\ & \Rightarrow(y-5)=\left(\frac{0-5}{2+3}\right)(x+3)\end{aligned}$ $\Rightarrow y=-x+2$ ...(1) Slope $=m=-1$ and slope of perpendicular line $=-\frac{1}{m}=1$ Equation of this line passing through $(3,3)$ is : $\begin{aligned} & (y-3)=1(x-3) \\ & \Rightarrow \quad y=x . \end{aligned}$ From eq. (1) we get, $\begin{aligned} & x=-x+2 \\ & \Rightarrow x=1 \text { and } y=1 . \end{aligned}$

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