Lesson 1.2.2

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

Basic

Finding a Midpoint

Find the midpoint of A(−4) and B(10).

Answer: The midpoint is at coordinate .

Intermediate

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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