A straight line passes through the points `(5,0)` and `(0,3)`. The length of perpendicular from the point `(4,4)` on the line is

Options

A. `(15)/(sqrt(34))`
B. `(sqrt(17))/(2)`
C. `(17)/(2)`
D. `sqrt((17)/(2))`

Answer

D

Explanation

The equation of line passing through points (5,0) and (0,3) is
`(y-0)=((3-0))/((0-5))(x-5)`
`impliesy=(3)/(-5)(x-5)`
`implies-5y=3x-15`
`implies3x+5y-15=0`
so, the length of perpendicular from the point (4,4) to the above line,
`d=((3xx4+5xx4-15))/(sqrt(3^(2)+5^(2)))`
`=(12+20-15)/(sqrt(9+25))=(17)/(sqrt(34))=sqrt((17)/(2))`