verify whether the points A (1,3), B(3,5) and C(-4,2) are collinear or not.
Answers
The distance formula is: √((x2-x1)2 + (y2-y1)2)
Three points (say, C, A, and B) are collinear if the distance CB = distance CA + distance AB
(note: in order to form a triangle, the sum of the lengths of two sides must exceed the length of the third side.)
Distance CB: √((-2-3)2 + (15-(-5))2)
√(25+400)
√425
5√17
Distance CA: √((-2-0)2 + (15-7)2)
√(4+64)
√68
2√17
Distance AB: √((3-0)2 + (-5-7)2)
√(9+144)
√153
3√17
Does distance CB = distance CA + distance AB ?
5√17 = 2√17 + 3√17
5√17 = 5√17 ? yes, points A, B, and C are collinear.