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 *x*, *y*, *z* elements of \(\mathbb{R}\), we have :

- d(
*x*,*y*) = 0 ↔*x*=*y*(separation axiom) - d(
*x*,*y*) = d(*y*,*x*) (symmetry) - d(
*x*,*y*) ≤ d(*x, z*) + d(*z*,*y*) (triangle inequality) - d(
*x*,*y*) = |*x*−*y*|.