Try this test:
0 0 0
5 5 6 6
1
1 1 2 2 1

Maybe test 5 is even more simple (I'm only sure that A, B and S lie on the same line and the answer is "Impossible"), but this test shows incorrectness of some logic.

0 0 10
4 0
100 0
1
1 -1 3 1 9

ans: 30 0
It's true.

BUT what in test #15?????