Midpoint

Midpoint

In a Cartesian plane, a point that divides a given line segment into a one-to-one ratio.

The coordinates of a midpoint can be found the same way as the point of intersection of a segment.

Example

The coordinates of the points are: $$\textrm{A}(x_1, y_1), \textrm{P}(x, y)$$ and $$\textrm{B}(x_2, y_2)$$.

Consider the points A(–2, –6) and B(6, 4).

The point P(2, -1) divides the segment AB into the rate k = 1.
The coordinates of the point P can be found like this:

$$x = \dfrac{6 + (-2)}{2} = 2$$

$$y = \dfrac{4 + (-6)}{2} = -1$$