If the point $\left[x_1+s\left(x_2-x_1\right),y_1+s\left(y_2-y_1\right)\right]$ divides the join of $\left(x_1,y_1\right)$ and$\left(x_2,y_2\right)$ internally, then

$P\left(x_1+s\left(x_2-x_1\right)\right),y_1+s\left(y_2-y_1\right)$

$P=\left[\frac{\left(1-s\right)x_1+s{x}_2}{1-s+s},\frac{\left(1-s\right)y,+s{y}_2}{1-s+s}\right]$

 P divides $A\left(x_1,y_1\right)\&B\left(x_2,y_2\right)$ in the ratio $s:1-s$ internally

$\Rightarrow \frac{s}{1-s}>0\Rightarrow s\left(s-1\right)>0$

$\Rightarrow \left(s-0\right)\left(s-1\right)<0$

$\Rightarrow 0<s<1$