A line perpendicular to the line segment joining the points (1, 0) and (2, 3) divides it in the ratio `1 : n`. Find the equation of the line.

Explanation

Slope of a line joining the points `(1,0)` and `(2,3)` is
`m_(1)=(3-0)/(2-1)=3`
If the slope of perpendicular line is `m_(2)` then
`m_(1)m_(2)=-1`
`implies m_(2)=-(1)/(3)`
Coordinates of the point dividing the line segment joining the points `(1,0)` and `(2,3)` in the ratio `1 : n` are
`=((1xx2+nxx1)/(1+n),(1xx3+nxx0)/(1+n))=((n+2)/(n+1),(3)/(n+1))`
Now, equation of line
`y-(3)/(n+1)=-(1)/(3)(x-(n+2)/(n+1))`
`implies 3(n+1)y-9=-(n+1)x+(n+2)`
`implies (n+1)x+3(n+1)y=(n+11)`