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Math Help - Coordinate Geometry: Finding the centroid of a triangle

  1. #1
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    Coordinate Geometry: Finding the centroid of a triangle

    The vertices of a triangle are the points P(5,6), Q(-4,3) and R(2,-3). Find the coordinates of the centroid. i.e. the point where the medians meet.

    is there an easier way to do this other than the rigorous method of finding the mid point of each side, and then finding the equation of the line and solving simultaenously?

    Thank you
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    Yes...

    Let A(x_1,y_1), B(x_2,y_2) and C(x_3,y_3) points on two dimensional plane.

    So, the centroid is given by:

    M(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})


    Try to prove it, not so hard.
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  3. #3
    MHF Contributor Also sprach Zarathustra's Avatar
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    Here you can read more about centroid... (really interesting stuff): http://www.mamikon.com/USArticles/EasyCentroids.pdf
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