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 on the number line. Here, P = -4 and Q = -1.
2. Recall that the distance between two points on a number line is the absolute value of the difference of their coordinates. The formula is: \(d(P, Q) = |x_Q - x_P|\).
3. Substitute the given coordinates into the formula: \(d(P, Q) = |-1 - (-4)|\).
4. Simplify the expression inside the absolute value: \(-1 - (-4) = -1 + 4\).
5. Calculate the absolute value of the result to find the distance: \(d(P, Q) = |3|\).

Key Concepts

Number Line and Coordinates

A number line is a visual representation of real numbers in order, where each point corresponds to a coordinate. Understanding how points are placed on the number line helps in determining distances between them by comparing their coordinates.

Distance Between Two Points on a Number Line

The distance between two points on a number line is the absolute value of the difference of their coordinates. This ensures the distance is always non-negative, calculated as |x2 - x1|, where x1 and x2 are the coordinates of the points.

Absolute Value

Absolute value measures the magnitude of a number regardless of its sign. It is used to find distances on the number line because distance cannot be negative, so |a| represents the distance of a from zero.