How to determine a point in a triangle with THIS special method (see link)?

Question

I am trying to get a working algorytm to check if a point is within a triangle.

I found this

https://stackoverflow.com/a/21510010/2429323

and i understand the first part of explanation. But i don't understand the rest. What does he mean with Xi Yj and Yk. Can Someone follow his thoughts and help me?

I would ask him personally, but it seems there is no PM possible, and i can't write a comment to (Reputation).