M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)Variables
- (x₁,y₁),(x₂,y₂): endpoints
- M: midpoint
How to use this formula
Finds the point halfway between two coordinate points.
Important notes
- Average corresponding coordinates.
Quick example
Between (0,2) and (4,6), M=(2,4).
Applicability, worked calculation, and verification
Domain and applicability
Use the midpoint formula for two points expressed in the same Cartesian coordinate system and compatible units.
Assumptions and domain checks
- Both endpoints use the same coordinate axes, scale, and units.
- The midpoint is obtained by averaging corresponding coordinates, not by averaging distances.
Do not use this formula when
- Do not use Midpoint Formula when the stated lengths, angles, or geometric conditions do not match the figure or use inconsistent units.
Boundary and special cases
- If the endpoints are identical, the midpoint must equal that same point.
- If one coordinate pair is symmetric about zero, the corresponding midpoint coordinate should be zero.
Equivalent and alternative forms
- In vector form, the midpoint can be written as M=(P_1+P_2)/2 when vector addition and scalar division are defined.
Worked example
For endpoints (−2, 4) and (6, 10), the midpoint is ((−2+6)/2, (4+10)/2) = (2, 7).
- List the two endpoints in the same coordinate order and confirm that their axes and units match.
- Add the two x-coordinates and divide that sum by two to obtain the midpoint x-coordinate.
- Add the two y-coordinates and divide that sum by two to obtain the midpoint y-coordinate.
- Verify the result by checking that the displacement from the first endpoint to the midpoint equals the displacement from the midpoint to the second endpoint.
Independent verification
Subtract the first endpoint from the midpoint and the midpoint from the second endpoint; the two displacement vectors should be identical.
Common mistakes
- Do not pair x₁ with y₂ or otherwise mix coordinate positions.
- Keep the factor of 1/2 on both coordinate sums and preserve negative signs inside parentheses.
Continue the workflow
Use Midpoint Formula in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right). - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-26
Review method: Reviewed the notation, variable definitions, applicability conditions, worked example, boundary cases, and independent verification method for Midpoint Formula.
Verified against: OpenStax Algebra and Trigonometry 2e
Automated quality check: Passed the core formula indexing gate.
Formula references
- Algebra and Trigonometry 2eOpenStax, Rice University — Reviewed algebra, functions, sequences, trigonometry, and analytic geometry definitions and examples.
Frequently asked questions
What is the Midpoint Formula used for?
Finds the point halfway between two coordinate points.
Can I copy this formula as LaTeX?
Yes. Copy M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right) or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.