Unit 8: Coordinate Geometry

8.1.1: Midpoint Formula

The Midpoint Formula

The midpoint between two points $\left(x_1, y_1\right)$ and $\left(x_2, y_2\right)$ is found by adding the coordinates together and dividing by two:

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

Example: The Midpoint Formula

What is the midpoint of $\overline{AB}$, where $A$ is $\left(-3, 7\right)$ and $B$ is $\left(5, -1\right)$?

We want the point halfway between $A\left(\underbrace{-3}_{x_1}, \underbrace{7}_{y_1}\right)$ and $B\left(\underbrace{5}_{x_2}, \underbrace{-1}_{y_2}\right)$.

$\begin{aligned} \left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right) &=\left(\frac{-3+5}{2},\frac{7-1}{2}\right) \\{}&=\left(\frac{2}{2},\frac{6}{2}\right) \\{}&=\left(1,3\right) \end{aligned}$