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

Correct Answer - D
The given line passes through (-3, 5) and (2, 0). Its equation is
`y-y_(1)=((y_(2)-y_(1))/(x_(2)-x_(1)))(x-x_(1))`
`implies (y-5)=((0-5)/(2+3)) (x+3)`
`implies y=-x+2` ...(1)
Slope `=m=-1`
and slope of perpendicular line `= -1/m=1`
Equation of this line passing through (3, 3) is :
`(y-3)=1 (x-3)`
`implies y=x`.
From eq. (1) we get,
`x=-x+2`
`implies x=1` and `y=1`.