A program to draw simple geometry (points, lines, dotted lines etc.)

If you do not like coding and looking for WYIWYG, then Ipe is a good option.

If you like coding, then you have many options: PSTricks, TIKZ/PGF, Metapost, Asymptote, ...

You may want to try Tikz. See http://www.texample.net/tikz/ for examples.

I use Omnigraffle for the Mac. It is by far the easiest figure-maker for mathematics and is LaTeX friendly. Simply drag and drop predefined shapes (including points, lines, polygons, etc.) within Omigraffle, adjust them as needed for size, opacity, color, etc., use LaTeXIt to add labels or equations, save, then export to pdf or eps. I created the following faithful reproduction of your image by sight in 45 seconds.