SOLUTION: Given AC=2(AB) Prove B is the midpoint of AC

Question 986481: Given AC=2(AB)
Prove B is the midpoint of AC
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

You can't prove that B is the midpoint of AC. Consider the following situation:

The measure of AC is 4 units and the measure of AB is 2 units. 2 times 2 is certainly 4, but B is certainly not the midpoint of AC.

Now if you had bothered to mention that B was located on the line segment AC, that would have been a different story. But that isn't what you asked, is it?

Extra credit: Why would it have been insufficient to state that A, B, and C are collinear?

John

My calculator said it, I believe it, that settles it

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