You are looking for what is called a "point in polygon" algorithm.  See http://en.wikipedia.org/wiki/Point_in_polygon.

A quick google for an R implementation gives:

http://www.rforge.net/doc/packages/SDMTools/pnt.in.poly.html

http://stat.ethz.ch/R-manual/R-devel/library/mgcv/html/in.out.html

On the other hand, I suspect this won't be the last time you'll need a developer.  This might be a good opportunity to learn to code by trying to implement this yourself.

Good luck!

Check  http://www.geeksforgeeks.org/how-to-check-if-a-given-point-lies-inside-a-polygon/    for some ideas.

Thank you for your information, Hayford Tsikata.

For Evan Clark: Thank you for your helpful suggestions, I solved the problem through the webpage you provided.

I solved this problem in the early 1980's with an algorithm written in Fortran. The application involved GIS. I may have complete documentation. I'll try to locate it, if you request it.

Otherwise, the answers above are all correct.

Goggalize : "point in polygon" and "r point in polygon".

The web sites that I got are:

http://en.wikipedia.org/wiki/Point_in_polygon

http://de.wikipedia.org/wiki/Punkt-in-Polygon-Test_nach_Jordan

http://alienryderflex.com/polygon/

http://www.rforge.net/doc/packages/SDMTools/pnt.in.poly.html

Luckily for you, some R programmer has already implemented the code.

You can consider points as edges in a graph and polygon as edges length; if length of edge is finite it is in polygon otherwise length of edge is infinite then it is out of polygon refer finding out length of an edge formula in graph theory of finite graphs.....N V Nagendram