Barycentric Coordinates of Point inside 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 an arbitrary point inside $T$.

Then the barycentric coordinates of $p$ with respect to $T$ are all positive.

Proof

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Sources

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