How do you calculate the distance between two points ‘a’ and ‘b’ on the real line?

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The distance between two points on the real number line, ‘a’ and ‘b’, is calculated using a simple mathematical formula. This distance, denoted as d(a, b), is found using the absolute difference between the two points.

The formula for computing this distance is:

d(a, b) = |a - b|

Here’s how it works:

  • If ‘a’ is greater than ‘b’, the formula effectively subtracts ‘b’ from ‘a’, giving you a positive result due to the absolute value.
  • If ‘b’ is greater than ‘a’, the operation is reversed, but the absolute value ensures that your answer remains positive.

This way of measuring distance ensures that we treat the two points symmetrically, regardless of their order on the number line.

For example, if we have two points: a = 3 and b = 7, the distance between them would be:

d(3, 7) = |3 - 7| = |-4| = 4

Conversely, if we take a = 7 and b = 3, we would still find:

d(7, 3) = |7 - 3| = |4| = 4

This demonstrates that regardless of the values of ‘a’ and ‘b’, the distance remains consistent. Understanding this concept is fundamental in various fields, including mathematics, physics, and even computer science, making it a crucial tool for problem-solving.

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