Midpoint Formula on a Coordinate Plane
Extend the midpoint idea to two dimensions — average both and coordinates.
Introduction
On a coordinate plane, every point has two coordinates. The midpoint formula averages each coordinate separately to find the center of a segment.
Past Knowledge
Number line midpoint (1.2.2). Ordered pairs.
Today's Goal
Find the midpoint of a segment on the coordinate plane and solve for missing endpoints.
Future Success
The Distance Formula (1.2.4) and partitioning segments (1.2.5) build on this.
Key Concepts
The 2D Midpoint Formula
Given and , the midpoint is:
Think: Average, Average
Average the x-coordinates for the midpoint's . Average the y-coordinates for the midpoint's .
Worked Examples
Computing a Midpoint
Find the midpoint of and .
Answer:
Finding a Missing Endpoint
M(5, 1) is the midpoint of where . Find .
For x:
For y:
Answer:
Common Pitfalls
Mixing Coordinates
Average x with x and y with y separately. Don't cross-mix: is wrong.
Real-Life Applications
Centre of a Map
Two cities plotted on a map with coordinates. The midpoint gives the ideal location for a new meeting venue equidistant from both cities — GPS apps use exactly this calculation.
Practice Quiz
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