In this situation, I've used the "Slice By Plane" option. I'll "V" snap the end points of the line, then immediately "Shift+Tab" to the "Z" coordinate field and enter a height such as 10 to define the 'plane'.
You could also give the line a thickness, then use the corners as snap points for "Slice By Plane". More accurate than my first suggestion.
Lastly, if you have a recent Pro edition, you could use the "Slice By Surface" option with the thickened line (or polyline/arc/curve).
Designer, Deluxe, (Basic, Expert, Professional), Platinum
Windows 10 Pro (1909), 64-bit