Question

The ratio in which the line $3x+y=9$ divides the line sequent joining the points $(1,3)$ and $(2,7)$ is given by

• A. $4:3$
• B. $3:4$
• C. $2:3$
• D. $3:2$

Answer 1

The correct option is B $3:4$

Let the line $3x+y-9=0$ divide the line segment joining the point $(1,3)$ and $(2,7)$ in the ratio $K:1$ at point $C$.

So, by section formula $C=(\frac{2K+1}{K+1},\frac{7K+3}{K+1})$

$C(\frac{2K+1}{K+1},\frac{7K+3}{K+1})$ lies on the line $3x+y-9=0$

$\therefore 3\left(\frac{2K+1}{K+1}\right)+\left(\frac{7K+3}{K+1}\right)-9=0$

$\Rightarrow 6K+3+7K+3-9K-9=0$

$\Rightarrow 4K-3=0$

$\Rightarrow K=\frac{3}{4}$

Thus, the line $3x+y-9=0$ divide the line segment joining the point $(1,3)$ and $(2,7)$ in the ratio $3:4$.