Three Points Collinear Calculator
Method 1: Take two points to establish a straight line, calculate the analytical expression of the straight line. Substitute the coordinates of the third point to see if it satisfies the analytical expression (straight line and equation).
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 slope of AB and the slope of AC. If they are equal, the three points are collinear.
Method 4: Use Menelaos theorem.
Method 5: Use the axiom in geometry "If two non-coincident planes have a common point, then they have and only one common straight line passing through the point". It can be seen that: if the three points belong to two intersecting planes, the three points are collinear.
Method 6: Use the axiom (theorem) "There is and 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: Let A B C, prove that the area of △ABC is 0.