SOLUTION: Determine whether the three points are collinear. (5,-1), (-3,6), (4,-2)

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Question 650919: Determine whether the three points are collinear.
(5,-1), (-3,6), (4,-2)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Three or more points P1, P2, P3 are said to be collinear if they lie on a single+straight+line+L.
let's check it:
Solved by pluggable solver: To determine if 3 points lie in a line
The 3 points lie on a same plane. For all points to lie on a line they should satisfy the equation of a line. Hence any two points taken on a line should calculate to the same slope of a line.


In order to prove the 3 points to lie on a line, as there exists a unique line containing three points and every line has a unique slope.


Hence it will be sufficient to prove that the slope calculated taking 2 points at a time should be equal.


Slope of line taking points (X1,Y1) and (X2,Y2) is

slope+=+%28Y2-Y1%29%2F%28X2-X1%29


slope+=+%28%286--1%29%2F%28-3-5%29%29+=+-0.875 ........................(1)



Slope of line taking points (X3,Y3) and (X1,Y1) is

slope+=+%28Y3-Y1%29%2F%28X3-X1%29


slope+=+%28%28-2--1%29%2F%284-5%29%29+=+1 ........................(2)



From conditions (1) and (2)


The 3 points do not a same line.


For all points to lie on a line they should satisfy the equation of a line. Hence any two points taken on a line should calculate to the same slope of a line.


Here the slopes are unequal hence the points do not lie on same line.


To read more on equations of a line refer to articles on wikipedia



since your points do NOT lie on a single+straight+line, they are NOT collinear