Question

The line segment joining the points (1, 2) and (−2, 1) is divided by the line 3x + 4y = 7 in the ratio
(a) 3 : 4
(b) 4 : 3
(c) 9 : 4
(d) 4 : 9

Answer 1

(d) 4:9

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 $\left(\frac{-2m+n}{m+n},\frac{m+2n}{m+n}\right)$ that lie on the line.
3x + 4y = 7

$$\begin{gathered} 3\times \frac{-2m+n}{m+n}+4\times \frac{m+2n}{m+n}=7 \\ \Rightarrow -2m+11n=7m+7n \\ \Rightarrow -9m=-4n \\ \Rightarrow m:n=4:9 \end{gathered}$$