Distance Between Two Points on a Line

Distance Between Two Points on a Line

The distance between two points A and B on a line is the length of the line segment that joins points A and B.

The concept of distance is also used to refer to the range of an interval on a number line

Notation

The distance between the points A and B is written as: d(A, B) and is read as “the distance from A to B.”

Properties

For all xyz elements of \(\mathbb{R}\), we have :

  • d(xy) = 0   ↔   xy       (separation axiom)
  • d(xy) = d(yx)                 (symmetry)
  • d(xy) ≤ d(x, z) + d(zy) (triangle inequality)
  • d(xy) = |x − y|.

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