# how can i compute the $\lambda_1, \lambda_2, \lambda_3$ for a point in terms of barycentric coordinates?

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 $$P$$.

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 $$\lambda_1, \lambda_2, \lambda_3$$

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