This page is on the midpoint of a line. This topic is typically found in (Canadian) high school mathematics.
Suppose we are given a point \(A\) with the co-ordinate (\(x_1\), \(y_1\)) and a point \(B\) with the co-ordinate (\(x_2\), \(y_2\)). The line segment \(AB\) connects the point \(A\) to the point \(B\).
The midpoint \(C\) as the co-ordinate (\(x_m\), \(y_m\)) is the point on the \(AB\) line which is in the middle of the line. In other words, the distance from the midpoint to \(A\) is the same distance from the midpoint to \(B\).
To compute the midpoint \(C\) for two points (in the xy-plane) is simply:
\[(\dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2})\]
In the midpoint formula, we add up the two x-values and divide by 2 and we add up the y-values and divide by 2.
A picture image can be found online (not mine) such as this image.
Example One
Given the point \(A\) as (-5, 2) and the point \(B\) as (2, 3), the midpoint \(C\) on the line \(AB\) is:
\[( \dfrac{-5 + 2}{2}, \dfrac{2 + 3}{2}) = ( \dfrac{-3}{2}, \dfrac{5}{2})\]
Example Two
Suppose that the point \(A\) is (1, 4) and the point \(B\) is (2, 2), the midpoint \(C\) on the line \(AB\) is:
\[( \dfrac{1 + 2}{2}, \dfrac{4 + 2}{2}) = ( \dfrac{3}{2}, 3)\]
