Let A(1, 0) and B(2, 3) be the given points and D divides the line segment in the ratio 1 : n. Coordinates of point D is $\left(\frac{n+2}{1+n},\frac{3}{1+n}\right)$ Slope of line AB is $\frac{3-0}{2-1}$ = 3 Since CD ⊥ AB ∴ Slope of CD = $\frac{-1}{3}$ Required equation of line CD is $\left(y-\frac{3}{1+n}\right)$ = $\frac{-1}{3}\left(x-\frac{n+2}{1+n}\right)$ ⇒ $\frac{1}{3}x + y - \left[\frac{n+11}{3(n+1)}\right]$ = 0 ⇒ (1 + n)x + 3(1 + n)y = n + 11.