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 \(\Big(\frac{-2m+n}{m+n},\frac{m+2n}{m+n}\Big)\) that lie on the line 3x + 4y = 7
\(3 \times \frac{-2m+n}{m+n}+4\times\frac{m+2n}{m+n}\) = 7
⇒ - 2 + 11 n = 7 m + 7 n
⇒ - 9 m = - 4 n
⇒ m: n = 4 : 9
