Parallel line segments

In this article I will address some questions about a mathematical problem that my friend Patrizio Frederic, a researcher in statistics at the University of Modena, proposed to me. Given some parallel line segments, is there at least one straight line that passes through all of them? If there were many lines that solve the problem, can I choose a “best one” among all of them? I will fully address the first question. As for the second question, I will illustrate it with some “experimental” examples and suggest an outline for future explorations.