# Statement(s)
> [!NOTE] Statement 1 (Formula for collinearity of distinct points)
> Let $\mathbf{x},\mathbf{y},\mathbf{z}\in \mathbb{R}^n,$ then they are collinear iff $d(\mathbf{x},\mathbf{y})=d(\mathbf{x},\mathbf{z})+d(\mathbf{z},\mathbf{y})$up to permuting $\mathbf{x},\mathbf{y}$ and $\mathbf{z}.$
**Moreover**: if $\mathbf{x},\mathbf{y},\mathbf{z}$ are distinct and $\mathbf{z}=\lambda_{1}\mathbf{x}+\lambda_{2}\mathbf{y}$ with $\lambda_{1}+\lambda_{2}=1$ then $|\lambda_{1}|:|\lambda_{2}|=d(z,y):d(z,x)$
\* Diagram here \*
# Proof(s)
**Proof of statement 1:**
$\blacksquare$
# Application(s)
**Consequences**:
**Examples**:
# Bibliography