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)

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Identify the coordinates of points Q and R on the number line. Here, Q = -1 and R = 8.

Recall that the distance between two points on a number line is the absolute value of the difference of their coordinates.

Write the distance formula for points Q and R as \(d(Q,R) = |Q - R|\).

Substitute the coordinates into the formula: \(d(Q,R) = |-1 - 8|\).

Simplify the expression inside the absolute value to find the distance.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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 essential in distance calculations to ensure the result is positive, as distance cannot be negative. For example, |−3| = 3 and |5| = 5.

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