How to determine if a point ( x 3 ; y 3 ) lies on a line passing through points ( x 1 ; y 1 ) and ( x 2 ; y 2 )?

  • Do you have any ideas for solving this problem? If there is something to add to the question. - Tivyram
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    I remind the closing ones that simple questions are not prohibited even in the case when the author of the question obviously missed school mathematics. - Pavel Mayorov

1 answer 1

The equation of a line passing through the points (x1; y1) and (x2; y2) is usually written as

x - x1 y - y1 ------- = ------- x2 - x1 y2 - y1

To get rid of the division, you can convert the equation:

 (x - x1) * (y2 - y1) - (x2 - x1) * (y - y1) = 0

It remains to substitute a point here (x3, y3).

  • "usually written as" - the first time I see this form. The canonical equation looks different: (x - x1) / (x2 - x1) = (y - y1) / (y2 - y1) . Although, of course, they are equivalent, but the points in the canonical notation do not disappear - Andrey NOP
  • @AndreyNOP this option is not generalized to three or more points ... However, it also exists and is objectively better. Thank you for reminding. - Pavel Mayorov