The midpoint formula and the distance formula
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What are all the formulas in math? There are hundreds, too many to name here in all the categories of mathematics. Most of them are in geometry, for coordinate geometry, area, and volume.
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You can use coordinate grids formapsA graphAnd lots of other things but those are the 2 most common ones.
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The cartesian coordinate system is the basic coordinate system people are familiar with. If you were to plot a basic X Y graph, where X and Y increase towards infinity, you are graphing in the cartesian coordinate system. There are a few other popular coordinate systems for more advanced math, but they are rarely used by most people. (polar coordinate system is common for some calculus equations)