question_answer

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) \[(0,2)\]

D) \[(1,1)\]

Correct Answer: D

Solution :

[d] The given line passes through \[(-3,5)\] and (2, 0). Its equation is

\[y-{{y}_{1}}=\left( \frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} \right)(x-{{x}_{1}})\]

\[\Rightarrow (y-5)=\left( \frac{0-5}{2+3} \right)(x+3)\]

\[\Rightarrow y=-x+2\]                ?. (1)

Slope \[=m=-1\]

and slope of perpendicular line \[=-\frac{1}{m}=1\]

Equation of this line passing through (3, 3) is:

\[(y-3)=1(n-3)\]

\[\Rightarrow y=x.\]

From eq. (1) we get,

\[x=-x+2\]

\[\Rightarrow \,\,\,x=1\,\,and\,\,y=1.\]