Question 34
Let's consider on the Cartesian plane all pairs of distinct points $(A, B)$, each of which has both integer coordinates. Among these pairs of points, find all those for which there exist two distinct points $(X, Y)$ with both integer coordinates, such that quadrilateral $AXBY$ is convex and inscribed.
A quadrilateral is called convex if both of its diagonals lie inside the quadrilateral.
A quadrilateral is called convex if both of its diagonals lie inside the quadrilateral.