How do you determine if A(2, -3), B(1, 8) and C(-4, 2) are on the same line or not?

1 Answer
Alan P.
Dec 7, 2016

#A, B, and C# are on the same line if (and only if)
#"slope"(A:B)="slope"(B:C)#
In this case the points are not co-linear.

Explanation:

#"slope"(A:B)=(Delta_(AB)y)/(Delta_(AB)x) = (8-(-3))/(1-2) = -11#

#"slope"(B:C)=(Delta_(BC)y)/(Delta_(BC)x)= (2-8)/(-4-1)=6/5#

Although it is not recommended when the points are close to being co-linear (on the same line), in this case the points are so far from being co-linear that it could be demonstrated with a graph of the points:
enter image source here

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