# Point of Division

## Point of Division

In a Cartesian plane, a point P that divides a segment AB into a positive ratio $$k = \frac{\textrm{m}\space\overline{\textrm{AP}}}{\textrm{m}\space\overline{\textrm{PB}}}$$.

### Example

The coordinates of the points are: A(x$$_1$$, y$$_1$$), P(x, y) and B(x$$_2$$, y$$_2$$).

Consider the points A(–4, –8) and B(8, 8).

The point P(–1, –4) divides the segment AB into the ratio k = $$\dfrac{1}{3}$$, part to part.
The coordinates of point P were found like this:

• $$\dfrac{x \space – (-4)}{8 \space – x} = \dfrac{1}{3}$$, hence $$x = -1$$
• $$\dfrac{y \space – (-8)}{8 \space – y} = \dfrac{1}{3}$$, hence $$y = -4$$