Lengths of segments on number lines: Set 1

Learning Objectives Define a line segment and its endpoints on a number line. State and apply the Ruler Postulate to find the length of a segment. Calculate the length of a segment on a number line using the coordinates of its endpoints. Use the Segment Addition Postulate to find the length of a segment composed of smaller, collinear segments. Determine the coordinate of an unknown endpoint given the other endpoint and the segment length. Solve algebraic problems involving segment lengths and the Segment Addition Postulate. Define and identify congruent segments on a number line. How does a GPS calculate the straight-line distance between two locations? 🗺️ It all starts with the fundamental concept of measuring a segment on a simple number line! This tutorial will cover t...

TermDefinitionExample Number LineA line on which numbers are marked at regular intervals, used to represent and order real numbers. Each point on the line corresponds to a unique number.A ruler is a physical representation of a number line. CoordinateThe number that corresponds to a specific point on a number line.On a number line, if point P is at the number -5, the coordinate of P is -5. Line SegmentA part of a line that consists of two endpoints and all the points between them. A segment is named by its endpoints.The segment with endpoints A and B is denoted as \(\overline{AB}\). Length of a SegmentThe distance between the two endpoints of a segment. Length is always a positive value.The length of \(\overline{AB}\) is denoted as \(AB\). If A is at 2 and B is at 7, then \(AB = 5\). Coll...

Ruler Postulate (Distance on a Number Line) For any two points A and B on a number line with coordinates \(x_1\) and \(x_2\) respectively, the length of \(\overline{AB}\) is given by the formula: \(AB = |x_2 - x_1|\) Use this formula to find the distance between any two points on a number line. The absolute value ensures the result is always non-negative, as distance cannot be negative. Segment Addition Postulate If point B is between points A and C, then \(AB + BC = AC\). This postulate applies only to collinear points. It states that the lengths of two adjacent segments add up to the length of the total segment they form.