Working out whether a specific point is in a specified area - please help!

Hi everyone

First post. I apologise in advance if this question is a little elementary, but I hope you are able to help.

I am working on some travel sites and would like to try to work out whether a given point is in a given area.

Let's suppose I had longitude/latitude information for Manhattan's boundary. I have a series of co-ordinates which I join together by a straight line in order to define the area.

Now... let's suppose I am given co-ordinates for, let's say, the Empire State Building and Bronx Zoo. I want to be able to mathematically deduce whether these two points fall inside or outside the boundary. Obviously, in this case, the ESB does, and the BZ doesn't. But is that easy to work out automatically?

Please note, I am not a mathematician so really need an explanation of how to work this out that a non-mathematician would understand!

Thanks a lot,

Aaron