Question

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. $(1,1)$

Answer 1

Answer: (D)

$(1,1)$

Equation of line in intercept form is

$\frac{x}{a}+\frac{y}{b}=1$

x intercept $=2$

$\therefore a=2$

So, the equation of line is $\frac{x}{2}+\frac{y}{b}=1$

The line passes through the point $(-3,5)$

$\therefore \frac{-3}{2}+\frac{5}{b}=1$

$\therefore b=2$

So, the equation of line is $\frac{x}{2}+\frac{y}{2}=1$

$⟹x+y-2=0$

Let $(h,k)$ be the foot of perpendicular from $(3,3)$ on the line $x+y-2=0$

$\therefore \frac{h-3}{1}=\frac{k-3}{1}=-\frac{3+3-2}{1^2+1^2}$

$\therefore h=k=1$

So, the foot of perpendicular is $(h,k)=(1,1)$

Answer is option (D)