Midpoint Calculator
Find the midpoint of a segment, the point dividing it in a ratio m : n (the section formula), the other endpoint, the reflection of a point, or whether three points are collinear, exactly.
About the Midpoint Calculator
The midpoint is the average of the two endpoints' coordinates. More generally, the point dividing P₁P₂ internally in the ratio m : n is ((m x₂ + n x₁)/(m + n), (m y₂ + n y₁)/(m + n)); externally, replace n by −n. The midpoint is the case m = n.
Fractions stay exact, so (2, 3) and (5, 7) in the ratio 1 : 2 gives (3, 13/3), not 4.333….
The formula
M = ((x₁ + x₂)/2, (y₁ + y₂)/2); internal m : n: ((m x₂ + n x₁)/(m + n), (m y₂ + n y₁)/(m + n))
- External division
- ((m x₂ − n x₁)/(m − n), (m y₂ − n y₁)/(m − n))
- Other endpoint
- P₂ = 2M − P₁
Worked example
(1, 2) and (5, 10)
- M = (3, 6)
- Dividing in 1 : 3 internally: ((5 + 3)/4, (10 + 6)/4) = (2, 4)
Questions people ask
How do I find an endpoint from the midpoint?
Choose “Other endpoint”: it doubles the midpoint and subtracts the known end.
What does dividing externally mean?
The point lies on the line through P₁ and P₂ but outside the segment, with its distances to P₁ and P₂ in the ratio m : n.