Let the line segment joining the points (1, 2) and (− 2, 1) be divided by the line 3x + 4y = 7 in the ratio m:n.

Then, the coordinates of this point will be that lie on the line 3x + 4y = 7

⇒ - 2 + 11 n = 7 m + 7 n

⇒ - 9 m = - 4 n

⇒ m: n = 4 : 9