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
Find the mid-point of the line segment joining \((4,-6)\) and \((-2,8)\).
- \(\left(\dfrac{4+(-2)}{2},\ \dfrac{-6+8}{2}\right)\)
Answer: \((1,\ 1)\)
Common mistake
Subtracting instead of adding. The midpoint is the mean of the coordinates.
On your course
| Course | In the exam |
|---|---|
| Class 10 | Learn it: CBSE gives no formula booklet |
| Class 9 | Learn it: CBSE gives no formula booklet |
From our own CBSE Maths formula sheets, in our words.
Practise and revise
- Practise Class 10 Coordinate Geometry MCQs
- Revise Class 10 Coordinate Geometry
- Revise Class 9 Coordinate Geometry
- Print Class 10 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?
Class 10: learn it: CBSE gives no formula booklet. Class 9: learn it: CBSE gives no formula booklet. This comes from our own CBSE 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 CBSE Math Revision. Not produced or endorsed by CBSE or NCERT.