Point of Division
In a Cartesian plane, a point P that divides a segment AB into a positive ratio [latex]k = \frac{\textrm{m}\space\overline{\textrm{AP}}}{\textrm{m}\space\overline{\textrm{PB}}}[/latex].
Example
The coordinates of the points are: A(x[latex]_1[/latex], y[latex]_1[/latex]), P(x, y) and B(x[latex]_2[/latex], y[latex]_2[/latex]). Consider the points A(–4, –8) and B(8, 8).
The point P(–1, –4) divides the segment AB into the ratio k = [latex]\dfrac{1}{3}[/latex], part to part.
The coordinates of point P were found like this:
- [latex]\dfrac{x \space - (-4)}{8 \space - x} = \dfrac{1}{3}[/latex], hence [latex]x = -1[/latex]
- [latex]\dfrac{y \space - (-8)}{8 \space - y} = \dfrac{1}{3}[/latex], hence [latex]y = -4[/latex]