I recently read that the equation of a triangle can be expressed in the following form:
$$\vec{r}=u\vec{r_{1}}+v\vec{r_{2}}+w\vec{r_{3}}$$
Where $$u,v,w\in [0,1]$$
How is this equation derived? Is this a generalization of the equation of the line in vector form? Can this be extended for a quadrilateral, pentagon and so on?