# Midpoint of a Line Segment

### Coordinate Point

Here the point **(12,5)** is

12 units along, and 5 units up

We can use Cartesian Coordinates to locate a point by **how far along** and **how far up** it is:

And when we know **both end points** of a line segment we can find the **midpoint "M"** (try dragging the blue circles):

## Midpoint of a Line Segment

The midpoint is **halfway** between the two end points:

- Its
**x value**is halfway between the two x values - Its
**y value**is halfway between the two y values

To calculate it:

- Add both "x" coordinates, divide by 2
- Add both "y" coordinates, divide by 2

As a formula:

M = ( \frac{x_{A}+x_{B}}{2} , \frac{y_{A}+y_{B}}{2} )

### Example: What is the midpoint here?

Use the formula:

M = ( \frac{x_{A}+x_{B}}{2} , \frac{y_{A}+y_{B}}{2} )

M = ( \frac{(−3)+8}{2} , \frac{5+(−1)}{2} )

M = ( 5/2, 4/2 )

M = ( 2.5, 2 )