Barycentric Coordinates of Centroid of Triangle

Theorem

Let $\mathbf a$, $\mathbf b$ and $\mathbf c$ be the position vectors of the $3$ vertices of a triangle $T$ in the plane.

Let $p$ be the centroid of $T$.

Let $\alpha$, $\beta$ and $\gamma$ be the barycentric coordinates of $p$ with respect to $T$

Then:

$\alpha = \beta = \gamma = \dfrac 1 3$

Proof

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Sources

• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): barycentric coordinates