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!!

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

$\displaystyle \vec{OD} = \vec{OB} + \frac{\vec{BA}}{2} \Leftrightarrow \vec{OB} = \vec{OD} - \frac{\vec{BA}}{2} \\ Do \quad the \quad same \quad for \quad the \quad others \quad and \quad you \quad will \quad get \quad what \quad you \quad want \\ \frac{\vec{OA} + \vec{OB} + \vec{OC}}{3} = ...etc$

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

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

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

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.........

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? ............

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