How would you do coordinate geometry proofs?

Hint: Geometry proofs or coordinate proofs are very prevalent because they help us to understand a particular problem in many ways. Coordinate proofs have been given variables for coordinates instead of numerical values so that they can be used for any related set of values. Thus, we shall look into what are the requirements of implementing geometry proofs.

Complete step by step answer:
There are certain things which are to be taken care of while doing geometry proofs.
The geometry proofs are done on a plane known as the cartesian plane. It consists of four quadrants each of which has a different combination of positive and negative values of the x-axis and the y-axis. While plotting points on the cartesian plane, we must carefully mark the points and not get confused with the sign of the axis about which the point is to be marked.
We shall remember and use the basic formulae of coordinate geometry such as the distance formula, midpoint formula, section formula, etc to prove the more complex statements given in mathematical problems. We shall also keep in mind a few properties of the basic shapes like the rectangle, parallelogram, circle, rhombus, etc to use them further.
Therefore, following these points, we can easily do coordinate geometry proofs.

Note: Geometry proofs in coordinate plane connect algebra and geometry. There are various predefined shapes and figures in geometry. Sometimes, in mathematical problems, we encounter some unknown figures which are only based upon imagination. Therefore, in order to get a better understanding of the question and to solve the problem faster, geometry proofs are of great help.