Midpoint Formula
Midpoint of a line segment.
Formula
Variables
Example
Midpoint of (2, 4) and (6, 8) is ((2+6)/2, (4+8)/2) = (4, 6).
How it works
The midpoint formula finds the point exactly halfway between two endpoints of a line segment. It works because halfway means the x-coordinate and y-coordinate are each the average of the two endpoint coordinates, so the midpoint splits the horizontal and vertical change evenly. This gives the balance point of the segment on the coordinate plane.
When to use it
Use this formula whenever you need the center point of a segment in geometry, graphing, or coordinate geometry problems. It is also useful in real-world settings like finding the middle of a path, a map segment, or the center between two locations.
Worked example, step by step
Find the midpoint of (-3, 5) and (7, 1). Use M = ((x1 + x2)/2, (y1 + y2)/2) Substitute the values: M = ((-3 + 7)/2, (5 + 1)/2) Simplify: M = (4/2, 6/2) Compute the averages: M = (2, 3)
Common mistakes to avoid
- Adding the coordinates but forgetting to divide by 2
- Mixing up x- and y-values from the two points
- Using the midpoint formula when the problem actually asks for distance or slope
Did You Know?
The midpoint formula is just the average of the endpoints — halfway in x and halfway in y.
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