method 1: take two points to establish a straight line, and calculate the analytical formula of the straight line. substitute the coordinates of the third point to see if the analytical formula (straight line and equation) is satisfied.

method 2: let the three points be a, b, and c. use vectors to prove: λab=ac (where λ is a non-zero real number).

method 3: use the point difference method to find the ab slope and ac slope. if they are equal, the three points are collinear.

method 4: use menelaus’ theorem.

method 5: use the axiom in geometry "if two non-overlapping planes have a common point, then they have and only one common straight line passing through the point." it can be seen that if three points belong to two intersecting planes, then the three points collinear.

method six: use the axiom (theorem) "there is and is only one straight line parallel (perpendicular) to the known straight line through a point outside the straight line". in fact, it is the same method.

method 7: prove that the angle is 180°.

method 8: assume abc and prove that the area of ​​△abc is 0.