Point of Division

Point of Division

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


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 \(y = -4\)

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