(a) Show that the diagram constitutes a model in the Euclidean Plane for the ax-ioms given...

(a) Show that the diagram constitutes a model in the Euclidean Plane for the ax-ioms given in Example 1, Section 2.1, which has only 10 points. We repeat the axioms here for convenience:

Axiom 1: Each line is a set of four points.

Axiom 2: Each point is contained by precisely two lines.

Axiom 3: Two distinct lines which intersect do so in exactly one point.

(b) Is this axiom system categorical?