How to show something is polygonally path-connected using a directed line segment?

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Show that the Cut plane $ X={\mathbb{C}} {\setminus} ({-\infty},0] $ is polygonally path-connected by using a directed line segment in the form of ${\gamma}(t)=tz+(1-t)w $ for some interval $[w,z]$ and $0<t<1$