The category in which points, lines and planes belong to is:
Undefined terms.
<h2>Step-by-step explanation:</h2>
An axiomatic system is a system that consist of the undefined terms and the collection of the statements or axioms or postulates that are related to these undefined terms.
As we know that in mathematics or geometry we know that there are three undefined terms--
1) Point -- It represent just a location.
2) Line-- It is a line that consist of all the points and extends infinitely in both the directions.
3) Plane-- It is a two-dimensional figure which extends infinitely.