The midpoint of a line segment is the point exactly halfway between its two endpoints. Because it sits in the middle, each of its coordinates is simply the average of the matching coordinates of the endpoints.
The midpoint formula
For endpoints A(x1, y1) and B(x2, y2), the midpoint M is found by averaging separately:
Key idea
M = ( (x1 + x2) / 2 , (y1 + y2) / 2 )
Worked example
Find the midpoint of A(2, 4) and B(6, 8). M = ((2 + 6)/2, (4 + 8)/2) = (8/2, 12/2) = (4, 6).
Finding a missing endpoint
If you know the midpoint and one endpoint, you can work backwards. Suppose M(4, 5) is the midpoint of A(2, 3) and B. Then (2 + x)/2 = 4 gives x = 6, and (3 + y)/2 = 5 gives y = 7, so B = (6, 7).
Remember
- Add the two x-values and halve; do the same for y.
- The midpoint of a segment through the origin and (a, b) is (a/2, b/2).
- To find a missing endpoint: endpoint = 2 × midpoint − known endpoint.