I made the following observation and I am wondering if it is always true.

Let $x_1$, $x_2$, $x_3$ and $x_4$ be four positive integer points in the plane ($x_i\in\mathbb{Z^2_{\geq 0}}$) forming a convex quadrilateral and let $x=x_1+x_2+x_3+x_4$.
Then it seems it is always possible to write $x$ as the nonnegative integer combination of **at most three** integer points inside, or on the edges, of the convex quadrilateral.

**Example 1.** With $x_1=(0,1)$, $x_2=(0,3)$, $x_3=(2,1)$, $x_4=(2,3)$, we have $x=(4,8)$. And we can write $x$ as $x=2(2,1)+2(0,3)$.

**Example 2.** With $x_1=(0,2)$, $x_2=(1,3)$, $x_3=(3,0)$, $x_4=(5,1)$, we have $x=(9,6)$. And we can write $x$ as $x=(2,1)+2(2,2)+(3,1)$.

- Is this observation true, or is there any counterexample? EDIT: Following the answer of fedja: yes it is always true, and obvious after all.
- EDIT: In higher dimension $n\geq 3$, is it possible to generalize and say that the vector $x$, made of the sum of $2n$ integer points $x_i\in\mathbb{Z^n_{\geq 0}}$, can be written as the nonnegative integer combination of at most $2n-1$ integer points inside, or on the facets, of the convex polyhedron which has vertices $x_i$.

Thank you very much!