Question

Ratio in which the line $3x+4y=7$ divides the line segment joining the points $(1,2)$ and $(2,1)$ is:

• A. $3:5$
• B. $4:6$
• C. $4:3$
• D. None of these

Answer 1

The correct option is C $4:3$

The equation of the line joining the points $(1,2)$ and $(2,1)$ is given by:

$\frac{x-1}{1-2}=\frac{y-2}{2-1}$

$\therefore x+y=3$

$\therefore 3x+3y=9$ ....(1)

And, $3x+4y=7$ ....(2) ...Given

Subtracting eq(2) from eq(1), we get

$y=-2$

Substitute $y=-2$ in eq(2), we get

$x=5$

Therefore, the given line cuts the line joining the given points at $(5,-2)$, externally.

By section formula for external division,

$x=\frac{m{x}_2-n{x}_1}{m-n}$

$\Rightarrow 5=\frac{m2-n1}{m-n}$

$\Rightarrow 5m-5n=2m-n$

$\Rightarrow 3m=4n$

$\Rightarrow m:n=4:3$