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|
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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