The points whose co–ordinates are $x=x_1+t\left(x_2-x_1\right),y=y_1+t\left(y_2-y_1\right)$ divides the join of $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ in the ratio

$x=x_1+t\left(x_2-x_1\right),y=y+t\left(y_2-y_1\right)$

$x=\frac{\left(1-t\right)x_1+t{x}_2}{\left(1-t\right)+t},y=\frac{\left(1-t\right)+t{y}_2}{\left(1-t\right)+t}$

$\Rightarrow$  $p\left(x,y\right)$ divides join of $A\left(x{}_1,y_1\right)$ & $B\left(x{}_2,y_2\right)$  in the ratio  $t:1-t$

Ratio $=\frac{t}{1-t}$