Three points collinear, a mathematical term, belongs to geometric problems, refers to three points on the same line. Let three points be a, B and C, and prove by vector that λ AB = λ AC (where λ is a non-zero real number).
Method 1: Take two points to establish a straight line and calculate the analytical formula of the line. Substitute the third point coordinate to see if the analytical expression (straight line and equation) is satisfied.
Method 2: Let the three points be A, B, and C. Use vector proof: λAB=AC (where λ is a non-zero real number).
Method 3: Determine the AB slope and the AC slope by the difference method, which is equal to three points collinear.
Method 4: Use the Menelaus theorem.
Method 5: Using the axioms in geometry "If two non-coincident planes have a common point, then they have one and only one common line passing through the point." It can be known that if the three points belong to two intersecting planes, then three points Collinear.
Method 6: Use the public (determined) theory "There is a straight line and there is only one straight line parallel to the known straight line (vertical)". In fact, it is the same method.
Method 7: Prove that the angle is 180°.
Method 8: Set A B C to prove that the area of △ABC is 0.
Point A (x1,y1) = 1；2
Point B (x2,y2) = 4；5
Point C (x3,y3) = 2；3
Click "calculate" to output the result
Area= 1/2{ (x1 y2 + x2 y3 + x3 y1) - ( x2 y1 + x3 y2 + x1 y3) }
= 1/2{(5+12+4) - (8+10+3 )}
= 1/2(21 - 21)
= 1/2(0)
= 0Area = 0; Three-point collinear
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