Equal slope = collinear?

Geometry Level 1

Suppose we have points $A, B$ and $C$ , such that the slope between $A$ and $B$ is equal to the slope between $B$ and $C$ . Are $A, B$ and $C$ necessarily collinear points ?

Yes No

1 solution

Alexander Katz
Jul 31, 2018

Yes! We need the line between $A$ and $B$ to be the same as the line between $B$ and $C$ . The equal slope condition tells us that these two lines are parallel, but we also know that both of these lines pass through B! Thus, they are necessarily the same line, meaning $A, B, C$ are collinear.

Equal slope = collinear?

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