Find the given distances between points P, Q, R, and S on a number line, with coordinates -4, -1, 8, and 12, respectively. See Example 3. d (P, Q)

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 P and Q with coordinates a and b, the distance d is given by d = |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.

Coordinates of Points

Coordinates are numerical values that define the position of points on a number line or in a coordinate system. In this context, points P, Q, R, and S have specific coordinates (-4, -1, 8, and 12, respectively) that allow us to identify their locations. Understanding how to interpret and manipulate these coordinates is essential for solving distance-related problems.