Modern Geometry

[chiefsfan31]

I need some help writing a proof. I have tried for a long time and have no idea to where to begin. If anyone could help me that'd be great!

Axiom 1: There exist at least four distinct points, no three of which are collinear.
Axiom 2: There exists at least one line with exactly n(n>1) points on it.
Axiom 3: Given two distinct points, there is exactly one line incident with both of them.
Axiom 4: Given a line L and a point P not on L, there is exactly one line through P that does not intersect L.

Prove: In an affine plane of order n, there are exactly n^2 points and n^2+n lines.

 

[pka]

In the usual sequence of theorems in an affine plane, these two precede the theorem you have asked about.
i) Every line contains exactly n points.
ii) There are exactly n+1 lines on every point.

To do i) consider the line given by axiom 2 and any other line.
Consider two cases: the two are parallel; then the two intersect.