 Quote by Norwegian
I remind you that we are doing mathematics here. Being fairly confident is just not good enough.
...I suggest adding to your imagination the possibility of two slightly angled lines and a point somewhere in the middle, as well as other cases, where the shortest distance in question is not attained at any endpoint.
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Point taken, I was a bit hasty there. I suppose I shouldn't be so confident in my mental sharpness after an all-nighter.
Nonetheless, even if an endpoint isn't involved in the solution, looking at the slopes between P3 and the endpoints is still of value in reducing the number of computations in a brute force approach. Unless I'm just going nutty, of course.