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

detailed solution

Correct option is A

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 thecoordinates 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=(0−3)2+(0−2)2+(6−0)2=9+4+36=49=7Similarly ,BE=(0−3)2+(4−0)2+(0−3)2=9+16+9=34and  CF=(6−0)2+(0−2)2+(0−3)2=36+4+9=49=7