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)

Verified step by step guidance

1. Identify the coordinates of points Q and R. Point Q is at -1 and point R is at 8.
2. Use the distance formula for points on a number line, which is the absolute value of the difference between the coordinates of the two points. The formula is |x_2 - x_1|.
3. Substitute the coordinates of points Q and R into the distance formula. So, substitute -1 for x_1 (Q's coordinate) and 8 for x_2 (R's coordinate).
4. Calculate the difference 8 - (-1). Remember to account for the negative sign in front of 1.
5. Take the absolute value of the result from the previous step to find the distance 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.