SOLUTION: If AB = 2PB, then is P the midpoint of AB?

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Question 1204464: If AB = 2PB, then is P the midpoint of AB?
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Unfortunately there isn't enough info.

If P was on segment AB and AB = 2*PB, then P would be the midpoint.

Or if we had right triangle PAB where AB = 2*PB, then we'd have a 30-60-90 triangle.
short leg = PB
long leg = AP
hypotenuse = AB
For any 30-60-90 triangle template, the hypotenuse is twice as long compared to the short leg.

Answer by ikleyn(52916) About Me  (Show Source):
You can put this solution on YOUR website!
.

Even if A, B and P are the points on one line (are collinear), it does not follow
from AB = 2PB that P is the midpoint of AB.

Because point P can lie outside of the interval AB.

Only if there is an additional information that point P is between points A and B
in the same line, then from AB = 2PB we can conclude that P is the midpoint of AB.