Finite projective plane properties

[quila]

Homework Statement

Let P be a finite projective plane so that all lines in P have the same number of points lying on them; call this number n+1, with n greater than or equal to 2. Show the following:

a) each point in P has n+1 lines passing through it.
b)the total number of points in P is n^2+n+1.
c) the total number of lines in P is n^2+n+1

Homework Equations

The Attempt at a Solution

I created a model of P using n=2. I showed that the number of points in P is 7 and the number of lines in P is 7. I tried to look for a way to generalize this problem but I am having trouble.

 

[Hurkyl]

Have you done the same exercise for affine planes? Can you use that info?