Question

Calculate the ratio in which the line segment joining $(3,4)$ and $(-2,1)$ is divided by the y-axis.

Answer 1

Using the section formula, if a point $(x,y)$ divides the line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m:n$, then

$(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$

Let the point on y-axis is $(0,y)$ and suppose it divides the segment in ratio $m:n$

Therefore,

$\frac{-2m+3n}{m+n}=0$

$\Rightarrow 3n=2m$

$\Rightarrow n=\frac{2m}{3}$

$\Rightarrow \frac{m}{n}=\frac{3}{2}$

$\therefore$ the ration is $m:n=3:2$