Sorry, I wanted to write a little more, but then got distracted.

Basically floating point numbers are not precise. A computer can only hold a limited number of digits (here binary digits). E.g. executing the following C++ code gives 0.6666666865.

cout << fixed << setprecision(10);
cout << (float)2 / 3 << '\n';

Therefore normally if you do some floating point arithmetik, then all your intermediate results will be slightly wrong, and you cannot compare values with == any more. E.g. the following code will assign b with false, since for the computer 0.3 * 3 + 0.1 will actually be slightly less than 1.

bool b = (0.3 * 3 + 0.1) == 1

If you want to compare two floating point values, you have to do it using a small epsilon.

if (abs(x - y) < 1e-8)
// instead of 
if (x == y)

Another thing. Always use double instead of float!

Now to your code. I did some little testing, and actually this floating point problem might not actually be the case why your code doesn't work. Sorry. I guess I was a little bit to quick by judging your code.

Here's some small test case for you:

2 0 0
0 1
0 -1

Your code returns 2, although clearly all three points are on 1 line. The reason is, that 1/0 will give +infinity, and -1/0 will give -infinity. So you have to handle that case separately.