Axioms of analytical geometry

Question

The approach in analytic geometry is somewhat different. We define concepts such as point, line, on, between, etc., but we do so in terms of real numbers, which are left undefined. The resulting mathematical structure is called an analytic mode1 of Euclidean geometry. In this model, properties of real numbers are used to deduce Hilbert’s axioms. This is a statement from Apostol Calculus. Is there any resource which develops analytical geometry this way? First define the objects we use and verify these are compatible with Hilbert's axiom.