The Midpoint Formula
In One Dimension
On a number line, the number halfway between x1 and x2 is
Example:
Find the midpoint between –1 and 4.
Use the formula. The midpoint is
(–1 + 4)/2
= 3/2 or 1.5.
In Two Dimensions
Suppose you are given two points in the plane (x1, y1) and (x2, y2), and asked to find the point halfway between them. The coordinates of this midpoint will be:
An easy way to think about this is that the x-coordinate of the midpoint is the average of the x-coordinates of the two points, and likewise with the y-coordinate.
Example:
Find the midpoint between (–2, 5) and (7, 7).
Use the formula. The coordinates of the midpoint are:
Simplify.
In Three Dimensions
It's pretty easy to guess based on the last two formulas!
In 3-dimensional space, the midpoint between (x1, y1, z1) and (x2, y2, z2) is
