Midpoint Formula on a Number Line
The midpoint is the exact middle of a segment — the point that splits it into two equal halves.
Introduction
Finding the middle of a segment on a number line is as simple as averaging two coordinates.
Past Knowledge
Ruler Postulate & segment length (1.2.1).
Today's Goal
Calculate the midpoint of a segment on a number line and solve for unknown endpoints.
Future Success
The 2D Midpoint Formula (1.2.3) extends this to the coordinate plane.
Key Concepts
Midpoint on a Number Line
If has coordinate and has coordinate , the midpoint has coordinate:
This is simply the average of the two coordinates.
Key Property
The midpoint divides the segment into two congruent parts: .
Worked Examples
Finding a Midpoint
Find the midpoint of A(−4) and B(10).
Answer: The midpoint is at coordinate .
Finding a Missing Endpoint
M is the midpoint of . A is at 2 and M is at 7. Find B.
Answer: is at coordinate .
Common Pitfalls
Subtracting Instead of Adding
The midpoint formula adds the coordinates, then divides by 2. Don't confuse this with the distance formula, which subtracts.
Real-Life Applications
Meeting in the Middle
Two friends live at mile markers 12 and 38 on the same highway. The fair meeting point? — mile marker 25.
Practice Quiz
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