# 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 amplitude 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|.