MathNet 2022-part-06 — 196 problems (EN–VI) Question 132

In the Cartesian plane, let $A=(0,0)$, $B=(200,100)$, and $C=(30,330)$. Compute the number of ordered pairs $(x, y)$ of integers so that $\left(x+\frac{1}{2}, y+\frac{1}{2}\right)$ is in the interior of triangle $ABC$.