Midpoint Of A Line

This topic will be 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.

Here is a diagram as a reference.

Source: http://images.tutorvista.com/cms/images/113/midpoint-formula.png


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:

    \[( \dfrac{1 + 2}{2}, \dfrac{4 + 2}{2}) = ( \dfrac{3}{2}, 3)\]

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