The coordinates of the midpoint of a line segment are the arithmetic means of the coordinates of the endpoints of the segment. Thus, if the endpoints are $(x_1,\,y_1)$ , and $(x_2,\,y_2)$ then the midpoint is $$\left(\frac{x_1\!+\!x_2}{2},\, \frac{y_1\!+\!y_2}{2}\right)\!.$$

For justifying the above coordinates of the midpoint, we know that its abscissa $x_0$ halves on the $x$ axis the line segment between $x_1$ and $x_2$ Since the lengths of the half-segments are $x_0\!-\!x_1$ and $x_2\!-\!x_0$ if $x_1 < x_2$ and their opposite numbers, if $x_2 < x_1$ in any case we can write $$x_0-x_1 = x_2-x_0.$$ Solving this equation for $x_0$ yields: $\displaystyle x_0 = \frac{x_1\!+\!x_2}{2}$ Similar result is gotten for the ordinate of the midpoint.