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.
Worked example
\(M(5,1)\) is the midpoint of \(AB\), where \(A\) is \((3,-4)\). Find \(B\).
- \(x_B=2(5)-3\), \(y_B=2(1)-(-4)\)
Answer: \(B=(7,\ 6)\)
Common mistake
Subtracting instead of adding. The midpoint is the mean of the coordinates.
On your course
| Course | In the exam |
|---|---|
| Edexcel 4MA1 (Higher) | Not given: learn it |
| Cambridge 0580 | Not given: learn it (Extended only) |
From our own IGCSE Maths formula sheets, in our words. Official: Pearson's 4MA1 specification (PDF, Appendix 5) · Cambridge's 0580 syllabus (PDF).
Practise and revise
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?
Edexcel 4MA1 (Higher): not given: learn it. Cambridge 0580: not given: learn it (Extended only). This comes from our own IGCSE 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 IGCSE Math Revision. Not produced or endorsed by Pearson Edexcel.