Midpoint formula: M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
The midpoint formula is M = ((x₁ + x₂)/2, (y₁ + y₂)/2).
What each letter means
- \(M\) the midpoint of the line segment
- \((x_1,\ y_1),\ (x_2,\ y_2)\) the two ends
When to use it
To find the point halfway between two points: the centre of a circle from a diameter, or a point on a perpendicular bisector.
In 3D add a third coordinate, (z₁ + z₂)/2.
Worked example
Find the midpoint of \((-2,7)\) and \((6,-3)\).
- \(\left(\dfrac{-2+6}{2},\ \dfrac{7+(-3)}{2}\right)\)
Answer: \((2,\ 2)\)
Common mistake
Subtracting instead of adding. The midpoint is the mean of the coordinates.
On your course
| Course | In the exam |
|---|---|
| AA SL | In the IB formula booklet |
| AI SL | In the IB formula booklet |
| AA HL | In the IB formula booklet |
| AI HL | In the IB formula booklet |
From our own IB Maths formula sheets, in our words. The IB gives its booklet to schools, so we checked against our own copy: your teacher has the official one. Official: IB DP Mathematics page.
Practise and revise
- Practise AI SL coordinate geometry questions
- Practise AA SL equations of straight lines questions
- Revise 3D geometry (AI SL)
- Print AA SL one-page formula sheet
Questions
What is the midpoint formula?
The midpoint formula is M = ((x₁ + x₂)/2, (y₁ + y₂)/2). M: the midpoint of the line segment; (x₁, y₁), (x₂, y₂): the two ends.
Is the midpoint formula given in the exam?
AA SL: in the IB formula booklet. AI SL: in the IB formula booklet. AA HL: in the IB formula booklet. AI HL: in the IB formula booklet. This comes from our own IB Maths formula sheets; your teacher has the official booklet.
How do I find an end point from the midpoint?
Double the midpoint and subtract the known end: x₂ = 2x_M − x₁, and the same for y.
Our own wording, examples and card, checked by IB Math Revision. Not produced or endorsed by the International Baccalaureate Organization.