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Math Help - Vector Proof for the Centroid of a triangle. Not a clue

  1. #1
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    Vector Proof for the Centroid of a triangle. Not a clue

    The medial triangle of a triangle ABC is the triangle whose vertices are located at the midpoints of the sides AB, AC, and BC of triangle ABC. From an arbitrary point O that is not a vertex of triangle ABC, you may take it as a given fact that the location of the centroid of triangle ABC is the vector (vector OA + vector OB + vector OC)/3
    I am to use vector techniques to prove that a triangle and its medial triangle have the same centroid, stating each step of the proof.
    I don't know where to begin with Vector Proofs...
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  2. #2
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    Re: Vector Proof for the Centroid of a triangle. Not a clue

    Hello, sloanjg!

    Here is a hint.

    Code:
                    A
                    o
                   *  *
                  *     * 
                 *        *
              D *           *  F
               o  *  *  *  *  o
              *  *           *  *
             *     *        *     *
            *        *     *        *
           *            * *           *
        B o  *  *  *  *  o  *  *  *  *  o C
                         E
    We have triangle ABC and medial triangle DEF.

    Note that: . FE \parallel AB and FE = \tfrac{1}{2}AB
    . . That is: . \overrightarrow{FE} \,=\,\tfrac{1}{2}\overrightarrow{AB}
    . . . .Also: . \overrightarrow{DF} \,=\,\tfrac{1}{2}\overrightarrow{BC}
    . . . . And: . \overrightarrow{DE} \,=\,\tfrac{1}{2}\overrightarrow{AC}

    Hope that helps . . .
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