Centroid means center.
Triangle Centroid -- from Wolfram MathWorld
Centroid means center.
Triangle Centroid -- from Wolfram MathWorld
There is no such thing as "the" center of a general triangle. A triangle has many different kinds of center just as a collection of numbers has many different kinds of average. There is a very extensive online encycolpedia about triangle centers here:
ENCYCLOPEDIA OF TRIANGLE CENTERS
The formulas it gives use either trilinear or barycentric coordinates which are both quite different from ordinary Cartesian coordinates.