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
(

n+2

1+n

,

3

1+n

)

Slope of line AB is

3−0

2−1

= 3
Since CD ⊥ AB
∴ Slope of CD =

−1

3

Required equation of line CD is
(y−

3

1+n

) = −

1

3

(x−(

n+2

1+n

)) ⇒

1

3

x+y−[

n+11

3(n+1)

] = 0
⇒ (1 + n)x + 3(1 + n)y = n + 11.