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

The correct option is 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.

The, the coordinates of this point will be $(\frac{-2m+n}{m+n},\frac{m+2n}{m+n})$ that lie on the line.

$3x+4y=7$

$3\times \frac{-2m+n}{m+n}+4\times \frac{m+2n}{m+n}=7$

$\Rightarrow -2m+11n=7n+7n$

$\Rightarrow -9m=-4n$

$\Rightarrow m:n=4:9$