We need to use variables to represent the vertices in a coordinate proof because this allows us to demonstrate that something holds no matter what numbers we use for the variables. If numbers are used for the x- and y-coordinates, we have only demonstrated that the theorem holds for that specific case. When we place figures on the coordinate plane to use for a coordinate proof, there are certain things that will help to make the problem easier. For example, when placing a square, rectangle or parallelogram, it can help to position one of the vertices at the origin.
Source: Integrated Mathematics 1 Notes
