Notion of distance for Euclidean plane

One motivation for developing axiomatic systems is to determine precisely which precisely which properties of certain objects can be deduced nom which other properties. The purpose is to choose a certain fundamental set of properties from which the other properties of the object can be deduced. Some of axioms of Euclidean plane based on the notion ef distance are considered. The notions of linear and planar sets are introduced in terms of distance. Thus Euclidean plane is regarded as a distance space with a metric satisfying the corresponding properties.