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i went through wiki, this post, this post and this video and am still confused about how to compute the lambda_1, lambda_2, lambda_3

per this post

$\lambda_1, \lambda_2, \lambda_3$ are the barycentric coordinates of $P$.

enter image description here

per this video, $$x = \dfrac{area_{PBC}}{area_{ABC}}$$ does that mean $\lambda_1 = \dfrac{area_{PBC}}{area_{ABC}}$ ?

in the context of this set of coordinates

[0.   0.   1.   0.25 0.25 0.5 ]
[0.   1.   0.   0.25 0.5  0.25]
[1.   0.   0.   0.5  0.25 0.25]

how to compute $\lambda_1, \lambda_2, \lambda_3$

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    $\begingroup$ $\lambda_1 : \lambda_2 : \lambda_3 = area_{PBC} : area_{PCA} : area_{PAB}$ and $\lambda_1 + \lambda_2 + \lambda_3 = 1 \implies (\lambda_1,\lambda_2,\lambda_3) = (x,y,z)$ $\endgroup$ – achille hui May 28 at 4:15

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