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GeomBench
Average the corners, find the balance point.
The centroid's coordinates are simply the mean of the three vertices' x-values and the mean of their y-values — no angles or side lengths needed, just averaging.
The centroid is the triangle's true center of mass — if cut from uniform material, it would balance perfectly on a pin placed exactly at this point, and it's also where all three medians (vertex-to-opposite-midpoint lines) intersect.
Centroid x
3
G = ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3)
What you entered
Centroid x = (x₁ + x₂ + x₃) ÷ 3
(0 + 6 + 3) ÷ 3= 3Centroid y = (y₁ + y₂ + y₃) ÷ 3
(0 + 0 + 6) ÷ 3= 2Result
Centroid x: 3
The centroid of the triangle with vertices (0, 0), (6, 0), (3, 6) is (3, 2).