Frequently Asked Questions
What is the centroid?
The intersection point of the three medians of a triangle. It is the arithmetic mean of the three vertex coordinates and the center of mass of a uniform triangular plate.
Is the centroid always inside?
Yes - unlike the orthocenter and circumcenter, the centroid always lies inside the triangle.
Centroid versus center?
For triangles, the centroid is the natural center for balance and arithmetic averaging, but the term center can refer to other special points depending on context (incenter, circumcenter, etc.).
How do you find the centroid of a triangle from coordinates?
Average the three vertices: the centroid is ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3). It is the balance point of the triangle and always lies inside it.
What is the difference between the centroid and the circumcenter?
The centroid is the center of mass (the average of the vertices, where the medians intersect); the circumcenter is the point equidistant from all three vertices. The centroid is always inside the triangle, but the circumcenter can fall outside an obtuse triangle.
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