# How to Find the Midpoint

## 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:

## Interactive Widget

Use this **interactive widget** to find the midpoint between two points. Start by clicking in the shaded area.

**Oops, it's broken!Turn your phone on its side to use this widget.**

## How to Find the Midpoint

Finding the midpoint between two points is easy.

### Question

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

### Step-by-Step:

# 1

Add the x-coordinates of the two points together. The x-coordinate of (1, 2) is **1**. The x-coordinate of (5, 4) is **5**.

1 + 5 = 6

# 2

# 3

Add the y-coordinates of the two points together. The y-coordinate of (1, 2) is **2**. The y-coordinate of (5, 4) is **4**.

2 + 4 = 6

# 4

Divide the answer (6) by 2.

6 ÷ 2 = 3

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

# 5

Write down the Cartesian coordinates of the midpoint as a pair of numbers in brackets, separated by a comma.

The x-coordinate (**3**) found in **Step 2** goes on the left.

The y-coordinate (**3**) found in **Step 4** goes on the right.

### Answer:

## How to Find the Midpoint Using a Formula

The midpoint between a point at **(x _{1}, y_{1})** and a point at

**(x**is found at:

_{2}, y_{2})The image below shows what we mean by x_{1}, y_{1}, x_{2} and y_{2}: