Affine space/Barycentric coordinates/Points/Example

Let ${\displaystyle {}P_{i}}$, ${\displaystyle {}i\in I}$, be an affine basis in an affine space ${\displaystyle {}E}$ over the ${\displaystyle {}K}$-vector space ${\displaystyle {}V}$. Then the point ${\displaystyle {}P_{j}}$ (${\displaystyle {}j\in I}$) has the barycentric coordinates ${\displaystyle {}(0,\ldots ,0,1,0,\ldots ,0)}$, where the ${\displaystyle {}1}$ is at the ${\displaystyle {}j}$-th place (${\displaystyle {}I}$ being finite and ordered).