Find the length of the medians of the triangle with vertices A(0, 0,6),B(0, 4,0) and C(6,0,0).

Find the length of the medians of the triangle with vertices A(0, 0,6),B(0, 4,0) and C(6,0,0).

  1. A

    7,7,34

  2. B

    7,8,34

  3. C

    7,9,34

  4. D

    None of these

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    Solution:

    ABC is a triangle with vertices A(0,0,6), B (0,4,0) and C (6,0,0).

    Let points D, E and F are the mid-points of BC, AC and AB, respectively. 

    So, AD , BE and CF will be the medians of the

    coordinates of point D=0+62,4+02,0+02=(3,2,0)

    Coordinates of point E=0+62,0+02,6+02=(3,0,3)

    and coordinates of point F=0+02,0+42,6+02

                                              =(0,2,3)

    Now, length of median AD = Distance between A and D 

    AD=(03)2+(02)2+(60)2=9+4+36=49=7Similarly ,BE=(03)2+(40)2+(03)2=9+16+9=34and  CF=(60)2+(02)2+(03)2=36+4+9=49=7

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