Find the ratio in which the straight line 2x + 3y – 20 = 0 divides the join of the points (2, 3) and (2, 10).

$\mathrm{Let} \mathrm{A}\left({\mathrm{x}}_1,{\mathrm{y}}_1\right)=(2,3),\mathrm{B}\left({\mathrm{x}}_2,{\mathrm{y}}_2\right)=(2,10)$
$\text{ Given line }\mathrm{L}\equiv 2\mathrm{x}+3\mathrm{y}-20=0$
$\begin{array}{l}{\mathrm{L}}_{11}=\mathrm{L}(2,3)=4+9-20=-7\\ {\mathrm{L}}_{22}=\mathrm{L}(2,10)=4+30-20=14\end{array}$
$\text{ The ratio in which }\mathrm{L}=0\text{ divides }\overline{\mathrm{AB}}$
$=-{\mathrm{L}}_{11}:{\mathrm{L}}_{22}=-(-7):14=1:2$