Let AD, BF and CF be the medians from vertex A, B and C to BC, CA and AB respectively.
∴ Co-ordinates of D =
\(\frac{0+6}{2},\frac{4+0}{2},\frac{0+0}{2}\) = (3 , 2 , 0)
Co-ordinates of E =
\(\frac{0+0}{2},\frac{0+4}{2},\frac{6+0}{2}\) = (3 , 0 , 3)
Co-ordinates of F =
\(\frac{0+0}{2},\frac{0+4}{2},\frac{6+0}{2}\) = (3 , 0 , 3)
∴ Length of AD =
\({\sqrt{{0-3)}^{2}+(0-2)^{2}+(6-0)^{2}}}\\=\sqrt{9+4+36}\\=\sqrt{49}\\=7\)
Length of BE =
\({\sqrt{{(0-3)}^{2}+(4-0)^{2}+(0-3)^{2}}}\\=\sqrt{9+16+9}\\=\sqrt{34}\)
Length of CF =
\({\sqrt{{(6-0)}^{2}+(0-2)^{2}+(0-3)^{2}}}\\=\sqrt{36+4+9}\\=\sqrt{49}\\=7\)
∴ Length of the medians are 7, \(\sqrt{34}\), 7
