Midpoint between two coordinates using a formula
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
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.