Geometry Lesson: Midpoint Formula

Using the Midpoint Formula


What is the midpoint formula? It's an algebraic tool to find the point halfway between two other points. If you imagine a line segment between two points, the midpoint lies exactly halfway along the line. Geometrically, you would say that it is equidistant from both points and lies on the line connecting those two points.

So, what IS the midpoint formula? Here you go:

$$ (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}) $$

And what does it tell you? Imagine you have two points. \(x_1\) represents the x-coordinate of the first point, and \(x_2\) represents the x-coordinate of the second point. Since you're dividing by 2, you're really just taking the average. The same applies for the y-coordinates.

So, wait -- I'm just taking the average? Yup! The midpoint between two points is just the average of the x-coordinates and the average of the y-coordinates.

Let's look at a quick example if you're not clear yet:

Example 1:

Find the point halfway between \((0,3)\) and \((4,7)\):

Remember the midpoint formula:

$$ (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}) $$

Plug in the appropriate values:

$$ (\frac{0+4}{2}, \frac{3+7}{2}) $$

And simplify for your solution:

$$ (2, 5) $$