Mathwords logoMathwords

Midpoint — Definition, Formula & Examples

Midpoint

The point halfway between two given points.

 

 

See also

Midpoint formula

Key Formula

M=(x1+x22,  y1+y22)M = \left(\frac{x_1 + x_2}{2},\; \frac{y_1 + y_2}{2}\right)
Where:
  • (x1,y1)(x_1, y_1) = Coordinates of the first endpoint
  • (x2,y2)(x_2, y_2) = Coordinates of the second endpoint
  • MM = The midpoint of the segment

Worked Example

Problem: Find the midpoint of the segment with endpoints A(2, 4) and B(8, 10).
Step 1: Average the x-coordinates of the two endpoints.
2+82=102=5\frac{2 + 8}{2} = \frac{10}{2} = 5
Step 2: Average the y-coordinates of the two endpoints.
4+102=142=7\frac{4 + 10}{2} = \frac{14}{2} = 7
Step 3: Combine the results to write the midpoint.
M=(5,  7)M = (5,\; 7)
Answer: The midpoint of segment AB is (5, 7).

Why It Matters

Midpoints appear throughout geometry—constructing perpendicular bisectors, finding centers of shapes, and proving triangles congruent all rely on locating midpoints. In coordinate geometry, the midpoint formula is a quick way to find the center of a line segment without measuring.

Common Mistakes

Mistake: Subtracting the coordinates instead of adding them.
Correction: The midpoint formula averages each pair of coordinates, so you add them first and then divide by 2. Subtracting gives you the difference between coordinates, not the halfway value.

Related Terms

  • Point — A midpoint is a specific type of point
  • Midpoint Formula — Formula used to calculate a midpoint
  • Line Segment — A midpoint divides a segment into equal halves
  • Distance Formula — Often used alongside midpoint in coordinate geometry
  • Bisect — To bisect a segment means to cut it at its midpoint