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. `sqrt17/2`
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)`
` Rightarrow y= 3/(-5) (x-5)`
` Rightarrow 3x+5y-15=0`
Now the length of perpendicular from the point (4,4) to the above line is
`d= (|(3xx4=5xx4-15)|)/(sqrt(3^(2)+5^(2)))=(|12+20-15|)/(sqrt(9+25))`
` (|17|)/sqrt34 = sqrt(17/2)`