The line have to be inside the set.
And we can generalize this.
Wow, this is very theoretical and interesting → we are building operations from atoms. (very similar to mathematics → like calculus).
Some operations → linear fractional mapping → preserves convexity. (such theories → amazing ideas!).
Dual or conjugate → do it twice → we end up to the location where we started → not always true but the language hinted. (very interesting). (the application side of this → relates to economic → operation optimization).