Intersection of the line through (0, 0) and (5, 5) and the line through (3, 0) and (0, 3).

We obtain (see the picture):

We can draw the figure with this script  (or with this - see the code;  se also here)

Intersection of the line through (0, 0) with direction 45° and the line through (3, 0) with direction −45°

Weget the same result.

If the lines do not intersect we get:

If the lines coincide: