Geometry!!
Affine Geometry on Nine Points

Axiom 1: There exists at least three noncollinear points.

Axiom 2: Every line contains at least two points.

Axiom 3: Each two points belong to at least one line.

Axiom 4: Given a line and a point not on it, there exists exactly one line containing that point that does not intersect the given line.

1. Draw a model of this geometry.
2. Prove the following theorem: Each point lies on exactly four lines.

Question

Geometry!!
Affine Geometry on Nine Points

Axiom 1: There exists at least three noncollinear points.

Axiom 2: Every line contains at least two points.

Axiom 3: Each two points belong to at least one line.

Axiom 4: Given a line and a point not on it, there exists exactly one line containing that point that does not intersect the given line. 

1. Draw a model of this geometry.
2. Prove the following theorem: Each point lies on exactly four lines.

anonymous · Answer

For number 1, see attached.

For number 2, try a proof by contradiction. Suppose there exists a point that does not line on 4 lines, then use the axioms and go from there.

anonymous · Answer

lie on 4 lines*. Typo, sorry.

anonymous · Answer

http://en.wikipedia.org/wiki/Finite_geometry#Finite_affine_and_projective_planes