What is the differences between a coordinate and non-coordinate geometry proof?

: What is the differences between a coordinate geometry proof and a proof method that does not require coordinat?
What is the differences between a coordinate geometry proof and a proof method that does not require coordinate geometry. When would it be appropriate to use a coordinate proof rather than another proof method?

Answers and Views:

Answer by Ben
The difference between the two is that in coordinate geometry, you have some way of finding the coordinates of any part of the shape in question. This is useful when your proof uses the fact that a line (especially one coming from the origin to some coordinate) can be split up into two parts: an x and y part. For a good example, see the proof of the law of cosines, which uses coordinate geometry in order to prove a more general version of the Pythagorean theorem using trigonometry and, confusingly, the Pythagorean theorem.