Midpoint Formula
Find the exact midpoint between two points using M = ((x₁+x₂)/2, (y₁+y₂)/2).
Step-by-step examples and explanation.
The Formula
M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
The midpoint formula finds the point exactly halfway between two given points.
It simply averages the x-coordinates and the y-coordinates separately.
Variables
| Symbol | Meaning |
|---|---|
| M | The midpoint (the result) |
| (x₁, y₁) | Coordinates of the first point |
| (x₂, y₂) | Coordinates of the second point |
Example 1
Find the midpoint between (2, 4) and (8, 10)
x₁ = 2, y₁ = 4, x₂ = 8, y₂ = 10
M = ((2 + 8) / 2, (4 + 10) / 2)
M = (10 / 2, 14 / 2)
M = (5, 7)
Example 2
Find the midpoint between (-6, 3) and (4, -9)
x₁ = -6, y₁ = 3, x₂ = 4, y₂ = -9
M = ((-6 + 4) / 2, (3 + (-9)) / 2)
M = (-2 / 2, -6 / 2)
M = (-1, -3)
When to Use It
Use the midpoint formula when:
- Finding the center of a line segment
- Locating the center of a circle given two endpoints of a diameter
- Dividing a segment into equal halves for construction problems
- Finding the average position between two data points