Vector proof - four points in space

AI Thread Summary
The discussion centers on a mathematical problem involving four points in space, A, B, C, and D, and their midpoints M and N. The goal is to prove that the equation AB + CB + CD = 4MN holds true. Some participants express confusion about the problem's validity, particularly when considering specific cases like a square. There is a suggestion that an additional point, AD, may be necessary for the equation to be accurate. The conversation highlights the need for clarity in the problem's formulation and the relationships between the points.
nc01
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The problem is: A, B, C, D are any four points in space. If M and N are the mid-points of AC and BD, show that AB + CB + CD = 4MN.

I'm not quite sure where to start. Could someone please help me?
 
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I'm not sure that the problem is correct. Suppose that A,B,C,D are the four corners of a square. In this case, M and N would both be the center of the square. This would make MN=0
 
welcome to pf!

hi nc01! welcome to pf! :smile:
nc01 said:
The problem is: A, B, C, D are any four points in space. If M and N are the mid-points of AC and BD, show that AB + CB + CD = 4MN.

?? :confused:

i think you need an AD in there …

AB + AD + CB + CD = 4MN :wink:​
 

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