Default package - Mimetex - is not very well documented 
but you can get some tips from Forkosh main site and test...
For example \picture(100){(50,50){\circle(99)} (0,30){\line(180,180)} (0,90){\line(180,-180)}}
gives
so yes - it is possible - but tools are not very "advanced" and it takes some time and effort to combine complex graphs.
See for example http://www.forkosh.com/mimetexmanual.html and there
(IIIf) \picture( ){ } "Environment", including \line( ){ } and \circle( )
Hi Muano, it took a little while but I figured that mimetex was the default package, so I went there first. the trouble is I got an issue with it. Simple but inelegant... so what has not been implemented? Or what have I not got right? I put this in:
$$$ \picture(100){(50,50){\circle(99)} (0,30){\line(180,180)} (0,90){\line(180,-180)}} $$$ and $$$ \line(180,180) $$$
Edit:I just got the same thing...wow, that was funny... OK, something at my end and not necessarily the server what have I not done?
You have done everything ok - I forgot that \line is one of the blacklisted tex commands in tex filter - to prevent endless lines or spirals ...
You can edit filter/tex/lib.php and remove
'\line',
from line 48 ( in function tex_sanitize_formula($texexp) )
I must stop sending these comments to moodle.org forums - what ever I say I need to add those 'but':s later 
Edit: Or if you want to keep \line blacklisted you can always install external cgi mimetex and use tags like http://www.imathas.com/cgi-bin/mimetex.cgi?\picture(100){(50,50){\circle(99)}+(0,30){\line(180,180)}+(0,90){\line(180,-180)}} to render such examples with editor image plugin (that's how I usually add these examples to forums)
Edit 2: + there is also an option to use some other tools outside moodle to create those images - for example http://www.imathas.com/editordemo/demo.html with IE and add the image address (mouse right click - properties) to editor image plugin or upload the images (graphs) as images without any script tags, applets etc if you are not allowed to use them
Your last comment seems the best option here.. I can create them in a Moodle I can make the necessary changes to then save the image and upload that. A pain for the moment, but better than nothing.
However, this comment, "...to prevent endless lines or spirals." does concern me a little.
I am thinking here that this becomes the improperly terminated loop? What happens? How is it fixed? A reboot of the server? Not possible, far too many Moodles on it.
It is for example possible to use some scripts to produce a huge amount of different graph images in a few seconds and this way attack the server or to produce some unparseable tags ( I have been able to do that since we got our first computers without any latex tags... 
) but I suppose \line is not one of the dangerous latex commands in most latex distributions.
For example in mimetex you can use value 600 for x slope and y slope and get
but if you try 601 you get
Different distributions of latex may have different rules for commands and because latexRender blacklisted originally \line (as well as \mbox) as potentially dangerous or unparseable command on some environments moodle did the same...
Now I can do that, I should be able to start a Trig page... If only my old Trig teachers could see this..hahahaaaa!!!!!! $ \picture(350,250){(25,25){\line(300,0)}(25,25){\line(0,220)}(25,245){\line(300,-220)}(310,25){\circle(100;135,180)}(20,100){\line(310,-75)} (25,25){\fbox{\line(5,5)}}(25,25){\line(150,150)}(165,140){Hypotenuse}(120,2){Adjacent}(2,80){\rotatebox{90}{Opposite}}(270,40){\theta}}$
Mimetex is actually pretty cool... BUT if you want to do the same with other distributions and tex filter you need some tuning...
Nice triangle, Colin!!!