Question 68
Let $M$ be a subset of a plane sufficing following properties:
1) There is no single line $k$, such that $M \subset k$.
2) For any parallelogram $ABCD$ if $A, B, C \in M$, then $D \in M$.
3) If $A, B \in M$, then $|AB| \gt 1$.
Prove, that there are two families of parallel lines, such that $M$ is a set consisting of all intersection points of lines from the first family with lines from the second family.
1) There is no single line $k$, such that $M \subset k$.
2) For any parallelogram $ABCD$ if $A, B, C \in M$, then $D \in M$.
3) If $A, B \in M$, then $|AB| \gt 1$.
Prove, that there are two families of parallel lines, such that $M$ is a set consisting of all intersection points of lines from the first family with lines from the second family.