Question

Find the coordinates of the point which divides the line segment joining $(3,4)$ and $(-6,2)$ in the ratio $3:2$ externally.

Answer 1

If $P(x,y)$ lies on $\overline{AB}$ (but not in between $A(x_1,y_1)$ and $B(x_2,y_2)$) such that $\overline{AP}:\overline{BP}=m:n$, then $P$ is said to divide $\overline{AB}$ externally in $m:n$ ratio.

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

Substituting $A(x_1,y_1)=(3,4)$ and $B(x_2,y_2)=(-6,2)$ in the above equation will give $P=(-24,-2)$