6 ms·
>You must also explain why there isn’t a third point on the line, and why that line’s existence is guaranteed, which is not obvious (at least to me). There isn
by stackghost 1mo ago
>You must also explain why there isn’t a third point on the line, and why that line’s existence is guaranteed, which is not obvious (at least to me).
There isn't a third point on the line you found because the problem stipulates that the set of points is not collinear.
- chenb4425 1mo agoThat's only assuming your set of points only contains three points. If you have four or more points, it's entirely possible that a line you draw between two points passes through a third. . ... If you're given the above set of points, it's obviously not collinear due to the point at the top, but if you draw a line through any of the bottom two points, it will hit a third.
- h3lp 1mo agoSo it says that not ALL points are on that single line. But it doesn't stipulate that THREE points can't be on the line---the theorem is about proving that you can find one that doesn't have the third point.