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 (Q, R)

Verified step by step guidance

1. Identify the coordinates of points Q and R on the number line. Here, Q is at -1 and R is at 8.
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: \(d(A, B) = |x_B - x_A|\).
3. Apply the distance formula to points Q and R: \(d(Q, R) = |8 - (-1)|\).
4. Simplify the expression inside the absolute value: \$8 - (-1) = 8 + 1$.
5. Calculate the absolute value to find the distance: \(d(Q, R) = |9|\).

Key Concepts

Distance on a Number Line

The distance between two points on a number line is the absolute value of the difference between their coordinates. This ensures the distance is always a non-negative number, representing the length between points regardless of direction.

Absolute Value

Absolute value measures the magnitude of a real number without regard to its sign. For any number x, |x| is the distance from zero on the number line, which is always non-negative, making it essential for calculating distances.

Coordinate Points on a Number Line

Points on a number line are represented by their coordinates, which are real numbers indicating their position relative to zero. Understanding these coordinates allows for straightforward calculation of distances and relationships between points.