Find the given distances between points P, Q, R, and S on a number line, with coordi-nates -4, -1, 8, and 12, respectively. d(Q,R)

Key Concepts

Distance on a Number Line

The distance between two points on a number line is calculated using the absolute difference of their coordinates. For points A and B with coordinates a and b, the distance d(A, B) is given by |a - b|. This concept is fundamental in understanding how to measure the separation between any two points in a one-dimensional space.

Absolute Value

Absolute value is a mathematical function that measures the distance of a number from zero on the number line, regardless of direction. It is denoted as |x|, where x is any real number. This concept is crucial when calculating distances, as it ensures that the result is always non-negative, reflecting the actual distance between points.

Coordinate System

A coordinate system provides a framework for identifying the position of points in space using numbers. In a one-dimensional number line, each point is represented by a single coordinate. Understanding how to interpret these coordinates is essential for solving problems related to distances, as it allows for the correct identification of points involved in the calculation.