| 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 slopes are equal hence the 3 points can lie on same line. If the slope calculated from points (X2,Y2) and (X3,Y3) comes out to be same then it is confirmed that the 3 points lie on a same line. From (1),(2) and (3) Hence, It is proved that the 3 points lie on same line. To read more on equations of a line refer to articles on wikipedia |