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# Midpoint between two coordinates using a formula
- URL: https://www.esheets.io/midpoint-between-two-coordinates-using-a-formula/
- Published: 2025-01-12T16:29:22.000Z
- Updated: 2026-06-21T17:12:15.000Z
- Author: Richard Linnington
- Tags: Maths, Algebra, Geometry and Shape

Finding the midpoint between two points is a useful skill in geometry and everyday life, like when you want to meet a friend halfway between two places. Using the midpoint formula makes it easy to calculate the exact middle point of a line segment on a coordinate plane. [Jump to the questions](#practise-now)

## Practise now

Worksheet preview and key skills 

### Worksheet preview

Practise midpoint between two coordinates using a formula with this self-marking maths worksheet.

The interactive worksheet below generates questions, gives instant feedback, and lets students record their score.

#### What you’ll practise

- Averaging the two x-coordinates.
- Averaging the two y-coordinates.
- Using the midpoint formula.
- Writing the midpoint as a coordinate pair.

Use the interactive worksheet below, or read the [Topic guide](#topic-guide) for the method and worked example.

Find the midpoint of the given coordinates. Remember to include brackets in your answer!

## Topic guide

### What this worksheet practises

This worksheet provides practice on calculating the exact midpoint between two coordinates algebraically, without using a visual grid. This requires applying the standard midpoint formula.

### Key method

The midpoint formula is essentially just finding the mean (average) of the x-coordinates, and the mean of the y-coordinates separately.

- Identify your two coordinate points: (x₁, y₁) and (x₂, y₂).
- **Find the middle x:** Add the two x-coordinates together, then divide the result by 2.
- **Find the middle y:** Add the two y-coordinates together, then divide the result by 2.
- Write your final answer as a new coordinate pair (x, y).

### Worked example

**Find the midpoint of the line connecting A(−4, 7) and B(8, 15).**

Step 1: Find the middle x-coordinate.

Add the x's: −4 + 8 = 4.

Divide by 2: 4 ÷ 2 = 2.

The middle x is 2.

Step 2: Find the middle y-coordinate.

Add the y's: 7 + 15 = 22.

Divide by 2: 22 ÷ 2 = 11.

The middle y is 11.

Step 3: Write the final coordinate.

The midpoint is (2, 11).

### Common mistakes to avoid

A very common mistake is subtracting the coordinates instead of adding them. Subtracting the coordinates is part of the formula for finding the *gradient*, not the midpoint. Always remember that the midpoint is an average, and finding an average always requires addition.

### Things to remember

Midpoints do not have to be whole numbers. If you add two coordinates and get an odd number (like 7 + 8 = 15), dividing by 2 will give you a decimal (7.5). This is perfectly normal and correct. Don't assume you've made a mistake just because the answer has a decimal point.