Midpoint of a Segment
Simple Explanation
The midpoint of a segment is the point exactly halfway between its two endpoints. Find it by averaging the x-coordinates and averaging the y-coordinates separately.
Why Do We Need It?
Midpoints let you find centre points — useful for balancing, dividing things equally, or finding the middle of any two locations.
See It
A coordinate plane with two draggable points and their midpoint marked and labelled
Formula
Midpoint Formula
M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
The point exactly halfway between two given points.
- M
- — the midpoint
- x₁, y₁
- — the coordinates of the first point
- x₂, y₂
- — the coordinates of the second point
When to use it: Whenever you need the exact centre point of a segment joining two known points.
Worked Example
Find a midpoint
Find the midpoint of the segment joining P(2, -3) and Q(8, 7).
Why Does This Work?
Averaging each coordinate finds the exact "balance point" in each direction independently — halfway horizontally and halfway vertically together give the point exactly halfway along the segment.
Real-Life Example
Meeting halfway
Two friends live at different points on a town map and want to meet at a fair, halfway location.
Averaging their coordinates gives a meeting point exactly halfway between their two homes.
Practice
What is the midpoint of the segment joining (0, 0) and (6, 10)?
EasyCommon mistake
Averaging an x-value with a y-value instead of averaging each coordinate with its own pair (mixing up (x₁+y₂)/2 with (x₁+x₂)/2).
Quick Review
- M = ((x₁+x₂)/2, (y₁+y₂)/2)
- Average the x-values and the y-values separately.
- The midpoint always lies exactly on the segment, halfway between the endpoints.