Find the lengths of the medians of the triangle with vertices A(0,0,6),B(0,4,0) and (6,0,0).
Let AD,BE and CF be the medians of the given △ABC.
Since AD is the median, D is the mid-point of BC.
∴ coordinates of point D= (0+62,4+02,0+02)=(3,2,0)
AD= √(0−3)2+(0−2)2+(6−0)2=√9+4+36=√49=7
Since BE is the median, E is the mid-point of AC.
∴ coordinates of point E= (0+62,0+02,6+02)=(3,0,3)
BE= √(3−0)2+(0−4)2+(3−0)2=√9+16+9=√34
Since CF is the median, F is the mid point of AB.
∴ coordinates of point F= (0+02,0+42,6+02)=(0,2,3)
Length of CF= √(6−0)2+(0−2)2+(0−3)2=√36+4+9=√49=7
Thus the lengths of the medians of △ABC are 7,√34 and 7 units.