How to determine whether or not three points are collinear.

Expert Answers
justaguide eNotes educator| Certified Educator

Three points are collinear if they lie on the same line. Given three points (x1, y1), (x2, y2) and (x3, y3) it can be determined if they are collinear or not by determining the equation of the line between any two points. The coordinates of the third point must satisfy the equation of the line that has been derived.

To illustrate this, the equation of the line through (x1, y1) and (x2, y2) is `(y - y2)/(x - x2) = (y2 - y1)/(x2 - x1)` .

If replacing x and y by x3 and y3 satisfies the equation, the three points are collinear or the points are collinear if `(y3 - y2)/(x3 - x2) = (y2 - y1)/(x2 - x1)` .