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Math Help - Triangle Problem

  1. #1
    Member aldrincabrera's Avatar
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    Triangle Problem

    Help me with this,.,.please

    Given a triangle with vertices at A,B,C, show that the point R = 1/3 (A+B+C) lies on each of the medians. thnx
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  2. #2
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    Re: Triangle Problem

    Quote Originally Posted by aldrincabrera View Post
    Help me with this,.,.please

    Given a triangle with vertices at A,B,C, show that the point R = 1/3 (A+B+C) lies on each of the medians. thnx
    Dear aldrincabrera,

    Take each median and find the point which divides it to the ratio 2:1 internally.

    Intuition: As you may know your point R is the centroid of the triangle. The centroid divides each median to the ratio 2:1 internally.
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  3. #3
    Member aldrincabrera's Avatar
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    Re: Triangle Problem

    .,.ammm.,.i'm a bit confused.,.,can u show me just the beginning of the step???thnx.,.,
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    Re: Triangle Problem

    Quote Originally Posted by aldrincabrera View Post
    .,.ammm.,.i'm a bit confused.,.,can u show me just the beginning of the step???thnx.,.,
    Refer to the figure that I have attached. Take the median drawn from the point A as AD. Let (x_a,y_a),(x_b,y_b)\mbox{ and }(x_c,y_c), be the coordinates of the vertices A,B and C respectively. Find the coordinates of D and then find the coordinates of E. I am sure you will be able to do this now.
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  5. #5
    Member aldrincabrera's Avatar
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    Re: Triangle Problem

    ,.,.thank u so much sir,.,.this really helped me a lot
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