Can anyone help me in Analytic Geometry?

Can anyone help me in Analytic Geometry?



I've been having a hard time understanding it. 
We are through with Forms of linear equations and Midpoint of Line segments. 
I still don't understand how ratios work. I mean if a line is a divided into let's say three parts, what ratios can I use to determine the the two points inside given both the endpoints? And my professor didn't teach us about the internal and exterbal parts so I don't know which I am solving. 
And what are the most essential formulas (please cite at least an example).. Thanks a LOT.





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