Please bear with me as this is my first ever post on here (although certainly not my first time here). I was wondering if anybody could help me get started on the following question:
Consider triangles in the plane with vertices at $(0,0)$, $(a,b)$ and $(x,y)$, where $a, b, x$ and $y$ are integers. Characterize, with proof, the integers $a$ and $b$ for which all such triangles that have $(a,b)$ as a vertex, has an area that is a positive integer.
I looked all over Math SE for a related question, but couldn't find anything (if there is a related question please correct me on this). I'm just hoping one of you kind souls would be willing to give me a hint as to where begin with this particular proof. From what I've seen, a question like this is fairly elementary as far as proofs go, but I am stuck nonetheless. This question isn't from any of my texts (the class is Intro to Abstract Algebra & Number Theory), but rather a question the professor wrote up himself. Like I said, I just need some help starting this guy off. Usually starting is the hardest part for me.
Any and all help is appreciated!