My attempt at a Vector Proof

[fredrick]

ABCD is a parallelogram. M is the midpoint of AB. P is the point of trisection of MD nearer to M. Prove that A, P,C are collinear and that P is a midpoint of trisection of AC.

Does this make much logical sense? anyhting i should alter?

[IMG]http://img152.imageshack.us/img152/5307/vectorproofsbm8.jpg[/img]
[IMG]http://img152.imageshack.us/img152/vectorproofsbm8.jpg/1/w757.png[/img]

[Ahmad]

I only briefly skimmed through this, but it could be easier to follow by implementing a few adjustments, although apart from a few structural points I do think it works out.

Firstly, words are your friend. Words can often express things more easily than math symbols, especially to explain in broad terms what you're doing. You don't have to have many words (yuck!) just a few which gives the reader a sense of direction. For example, you could mention to the reader that it suffices to prove that , which would prove both the collinearity of A, P and C, as well as that P trisects AC.

Secondly, you could structure your proof slightly better. For example, you said but this assumes A, P, C are collinear, which is to be proved. It's not hard to fix this.

Lastly, don't take my criticism too harshly, I think overall this is a good try, better than I've seen by a lot of people. In particular I like the diagram. 

[fredrick]

ok i understand that so i should of just stopped when i showed AP=(1/3)AC which shows the collinearity and that it also trisects.