Distance between two Points on the Real Number Line


The distance between two points on the real number line, also called the absolute difference, is the absolute value of the difference of the two points.

Definition:

Let a and b be any two points on a real number line, then the distance between a and b is given by |a - b| or |b - a|

Examples showing how to find the distance between two points on the real number line


Example #1

Find the distance between -6 and 8 on the real number line.

Solution

The distance between a and b is given by |a - b| or |b - a|

Let a  = -6 and b = 8

|a - b| = |-6 - 8| = |-6 + -8| = |-14| = 14

|b - a| = |8 - -6| = |8 + 6| = |14| = 14

Notice that the answer is the same for using |a - b| or |b - a|

Example #2

Find the distance between 4 and 9 on the real number line.

Solution

The distance between a and b is given by |a - b| or |b - a|

Let a  = 4 and b = 9

|a - b| = |4 - 9| = |4 + -9| = |-5| = 5

|b - a| = |9 - 4| = |5| = 5

Example #3

Find the distance between -10 and -2 on the real number line.

Solution

The distance between a and b is given by |a - b| or |b - a|

Let a  = -10 and b = -2

|a - b| = |-10 - -2| = |-10 + 2| = |-8| = 8

|b - a| = |-2 - -10| = |-2 + 10| = |8| =  8

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