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Maths traingle need help thanks!

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    Hey guyss
    Im really stuck on this question

    In a triangle ABC the points D, E, F trisect the sides so that BC = 3 BD, CA = 3 CE,
    and AB = 3 AF. Show that triangles ABC and DEF have the same centroid.

    Ok so i found the centroid of ABC which is (a-b/3,c/3)
    I did this buy plotting the triangle onto a x and y axis and having the coordinates

    A(-b,0)
    B(a,0)
    C(0,c)

    now i have to prove that the triangle DEF inside of triangle ABC has the same centroid but im having trouble getting the coordinates of triangle DEF

    HELP PLEASEE
    THANK YOU
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    If im wrong in the previous parts please correct me
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    anyone?
    im sad

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