| Solved by pluggable solver: To determine if 3 points lie in a line |
| The 3 points lie on a same plane. For all points to lie on a line they should satisfy the equation of a line. Hence any two points taken on a line should calculate to the same slope of a line. In order to prove the 3 points to lie on a line, as there exists a unique line containing three points and every line has a unique slope. Hence it will be sufficient to prove that the slope calculated taking 2 points at a time should be equal. Slope of line taking points (X1,Y1) and (X2,Y2) is Slope of line taking points (X3,Y3) and (X1,Y1) is From conditions (1) and (2) The 3 points do not a same line. For all points to lie on a line they should satisfy the equation of a line. Hence any two points taken on a line should calculate to the same slope of a line. Here the slopes are unequal hence the points do not lie on same line. To read more on equations of a line refer to articles on wikipedia |