Midpoint Formula
3D Midpoint M = ((x₁+x₂)/2, (y₁+y₂)/2, (z₁+z₂)/2)
Each coordinate of M is the average of the corresponding coordinates
Example
Points A(2, 6) and B(8, 4)
Midpoint x = (2+8)/2 = 5
Midpoint y = (6+4)/2 = 5
M = (5, 5)
Distance AB = √((8−2)²+(4−6)²) = √(36+4) = √40 ≈ 6.325
Uses of the Midpoint
- Bisector: The midpoint is the point where the perpendicular bisector of a segment crosses it
- Triangle centroid: The intersection of the three medians (each joining a vertex to the midpoint of the opposite side)
- Computer graphics: Finding the center of a line segment for rendering and collision detection
- Navigation: Finding the halfway point between two GPS locations
- Real estate: Finding a meetup point equidistant between two addresses
Frequently Asked Questions
Is the midpoint always on the line segment?
Yes — the midpoint formula gives a point that lies exactly on the line segment connecting the two endpoints, precisely halfway between them. It satisfies the parametric equation P(t) = P₁ + t(P₂−P₁) at t = 0.5.
How do I find the other endpoint if I know the midpoint?
Rearrange the midpoint formula: if M = ((x₁+x₂)/2, (y₁+y₂)/2), then x₂ = 2·Mx − x₁ and y₂ = 2·My − y₁. For example, if one endpoint is (3, 1) and the midpoint is (5, 4), the other endpoint is (2·5−3, 2·4−1) = (7, 7).
What is the difference between midpoint and median?
The midpoint is a geometric concept — the center point of a line segment. The median (in statistics) is the middle value in a sorted dataset. In geometry, a triangle median is a line segment from a vertex to the midpoint of the opposite side — so it uses the geometric midpoint concept.