# How to Find the Midpoint (Mathematics Lesson)

# Finding the Midpoint

The midpoint is half way between two points.We can find the Cartesian coordinates of the midpoint if we know the Cartesian coordinates of the two points, .

Imagine we wanted to find the midpoint between the points with Cartesian coordinates

**(1, 2)**and

**(5, 4)**. The image below shows what we mean by the midpoint:

# How to Find the Midpoint

Finding the midpoint between two points is easy.#### An Example Question

Find the midpoint between the points with Cartesian coordinates (1, 2) and (5, 4).Step 1

**1**. The x-coordinate of (5, 4) is

**5**.

1 + 5 = 6

Step 2

6 ÷ 2 = 3

**3 is the x-coordinate of the midpoint**.

Step 3

**2**. The y-coordinate of (5, 4) is

**4**.

2 + 4 = 6

Step 4

6 ÷ 2 = 3

**3 is the y-coordinate of the midpoint**.

Step 5

The x-coordinate (

**3**) found in

**Step 2**goes on the left.

The y-coordinate (

**3**) found in

**Step 4**goes on the right.

# How to Find the Midpoint Using a Formula

The midpoint between a point at**(x**and a point at

_{1}, y_{1})**(x**is found at:

_{2}, y_{2})The image below shows what we mean by x

_{1}, y

_{1}, x

_{2}and y

_{2}:

# A Real Example of How to Find the Midpoint

The slider below gives another example of how to find the midpoint of two points.##### Interactive Test

**show**

Here's a second test on finding the midpoint.

Here's a third test on finding the midpoint.

##### Note

# What Are Cartesian Coordinates?

Cartesian coordinates are used to describe the position of a point on a graph.Cartesian coordinates work by measuring how far across and how far up the point is from the origin.

# Why Does the Method Work?

The method works because it finds the point in the middle of the two points.The x-coordinate of the midpoint is just the average of the x-coordinates of the end points.

The y-coordinate of the midpoint is just the average of the y-coordinates of the end points.

**Remember**, the average of two numbers is found by adding them together and dividing by 2.

The average of two numbers is the number exactly half way between the two numbers.