Creating regions (set of lat, lng) on map using other than ArcMap?

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I'm writing a project for school and as a part of the project I need to tell if a certain point is within a given region (which is a polygon made of lat, lng tuples).

So far I was working with http://www.doogal.co.uk/polylines.php but unfortunately this isn't enough when I want to draw 50 areas, name them and keep them organized.

What's the easiest way to achieve what I need? I tried using ArcGIS's ArcMap but that seemed like a total overkill, it would take me too much time to learn how to work with this program and I don't need 99% of the features it provides.



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