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Math Help - Vector technique to prove a triangle and its medial have the same centroid.

  1. #1
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    Vector technique to prove a triangle and its medial have the same centroid.

    Can someone help with this problem.......please............and thanks in advance.......................Usevector techniques to prove that a triangle and its medial triangle have thesame centroid..............So far I have triangle ABC centroid = vector (OA+OB+OC)/3.................the medial triangle DEF centroid = vector (OE+OF+OD)/3.................Is this correct so far?...............I don't know how to proceed to prove .....or to make (OA+OB+OC)/3........ = ......(OE+OF+OD)/3.........help please!!
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    Re: Vector technique to prove a triangle and its medial have the same centroid.

    \vec{OD} = \vec{OB} + \frac{\vec{BA}}{2} \Leftrightarrow \vec{OB} = \vec{OD} - \frac{\vec{BA}}{2} \\ Do \quad the \quad same \quad for \quad the \quad others \quad and \quad you \quad will \quad get \quad what \quad you \quad want \\ \frac{\vec{OA} + \vec{OB} + \vec{OC}}{3} = ...etc
    Last edited by ManosG; May 5th 2013 at 11:28 AM.
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    Re: Vector technique to prove a triangle and its medial have the same centroid.

    Thanks for the reply..............how do I do that.............I am so confused
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    Re: Vector technique to prove a triangle and its medial have the same centroid.

    See my updated post
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    Re: Vector technique to prove a triangle and its medial have the same centroid.

    Thank you...........Thank you...........Thank you...........to infinity and beyond............lol.............this problem is so much clearer now..........okay I will continue......brb
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    Re: Vector technique to prove a triangle and its medial have the same centroid.

    Does the labeling of the triangles makes a difference?................my calculations seems weird.........
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  7. #7
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    Re: Vector technique to prove a triangle and its medial have the same centroid.

    Hhhhmmmpppppppp...........silly question .how do you account for the 3 in the denominator? ............
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  8. #8
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    Re: Vector technique to prove a triangle and its medial have the same centroid.

    What do you mean? Sorry, my mother-tongue is not English
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