Coordinate System and Coordinates
6.0 Section formulae
6.0 Section formulae
(a) If any point $P(x,y)$ divides the line joining $A({x_1},{y_1})$ and $B({x_2},{y_2})$ in the ratio $m:n$ internally then $$x = \frac{{m{x_2} + n{x_1}}}{{m + n}},{\text{ }}y = \frac{{m{y_2} + n{y_1}}}{{m + n}}$$
- When point $P(x,y)$ divides internally, the ratio $\frac{m}{n}$ is positive.
(b) If any point $P(x,y)$ divides the line joining $A({x_1},{y_1})$ and $B({x_2},{y_2})$ in the ratio $m:n$ externally then $$x = \frac{{m{x_2} - n{x_1}}}{{m - n}},{\text{ }}y = \frac{{m{y_2} - n{y_1}}}{{m - n}}$$
- When point $P(x,y)$ divides externally, the ratio $\frac{m}{n}$ is negative.
