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Question 1026078: Hello, Could someone please help me with this question? I have a triangle with A(0,0), B(0,2k), C(2h,0) and P(h,k) which is midpoint of BC. The question is, "is point A on the perpendicular bisector of BC? The choices are: Always, Never, Sometimes. I believe it is sometimes, but am not 100% sure. My reasoning is that P is the midpoint and bisects segment BC, and if you draw a line from A to P, it will bisect BC. Thanks for any help!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! I have a triangle with A(0,0), B(0,2k), C(2h,0) and P(h,k) which is midpoint of BC. The question is, "is point A on the perpendicular bisector of BC? The choices are: Always, Never, Sometimes. I believe it is sometimes, but am not 100% sure. My reasoning is that P is the midpoint and bisects segment BC, and if you draw a line from A to P, it will bisect BC.
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Plot the points::
A(0,0) is at the origin
B(0,2k) is on the y axis
C(2h,c) is on the x axis
P(h,k) is the midpoint of BC
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Looks like the answer is "always".
Cheers,
Stan H.
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