The Ruler Postulate & Segment Addition
Every segment has a measurable length. When a point sits between two endpoints, the whole equals the sum of the parts.
Introduction
A ruler assigns a real number to every point on a line, and the distance between two points is always positive. The Segment Addition Postulate lets us break a longer segment into smaller pieces and add up their lengths.
Past Knowledge
Segments & their notation (1.1.2). Postulates (1.1.5).
Today's Goal
Use the Ruler Postulate and Segment Addition Postulate to find unknown lengths.
Future Success
Midpoints (1.2.2) and the Distance Formula (1.2.4) extend these ideas to coordinates.
Key Concepts
The Ruler Postulate
Every point on a line can be paired with a real number (its coordinate). The distance between two points and with coordinates and is:
Segment Addition Postulate
If point is between points and , then:
Why Absolute Value?
Distance is always positive. Taking ensures we get the same answer regardless of which coordinate we subtract first.
Worked Examples
Using the Ruler Postulate
Point A has coordinate −3 and point B has coordinate 5. Find AB.
Answer:
Segment Addition
B is between A and C. , , . Find .
Answer: , so and .
Common Pitfalls
Forgetting the Absolute Value
Without , you might get a negative distance. Distance is always positive: .
Real-Life Applications
Road-Trip Distances
Highway mile markers are coordinates on a number line. The distance between marker 42 and marker 97 is miles. If you stop at marker 65, the Segment Addition Postulate tells you: 23 + 32 = 55 miles.
Practice Quiz
Loading...