Affine space/Barycentric coordinates/Points/Example

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