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(P, Q)

Verified step by step guidance

1. Identify the coordinates of points P and Q. Point P is at -4 and point Q is at -1 on the number line.
2. Understand that the distance between two points on a number line is the absolute difference between their coordinates.
3. Set up the distance formula for points on a number line: \(d(P, Q) = |P - Q|\).
4. Substitute the coordinates of P and Q into the formula: \(d(P, Q) = |-4 - (-1)|\).
5. Simplify the expression inside the absolute value and calculate the absolute value to find the distance.

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.

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 use these coordinates is essential for calculating distances between the points.