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

According to the section formula, the coordinates of the points that divides the line segment joining the points `(1,0)` and `(2,3)` in the ratio `1:n` is given by


`{(n(1)+1(2))/(1+n),(n(0)+1(3))/(1+n)}={(n+2)/(n+1),3/(n+1)}`


The slope of the line joining the points `(1,0)` and `(2,3)` is `m=(3-0)/(2-1)=3`


We know that two non vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.


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