Corner points by code

You will find the corner points of a region by solving every pair of boundary lines, as in the lesson. The checker tests four regions.

The idea. A rule is (a, b, c) for $ax + by \le c$. The boundary lines are the rules and the two axes. Two lines meet where the equations hold together. We use exact fractions, so a corner such as $\tfrac{9}{2}$ is not spoiled by rounding.

Your tasks.

1. Finish meet(line1, line2). Return the point (x, y) where the two lines meet, or None when they are parallel.
2. Finish corner_points(rules). Return the sorted list of different corner points.
3. Finish count_corners(rules). Return how many corner points there are.