Let vertices of the ΔABC be A(x1, y1, z1 ),B(x2 ,y2 , z2 ) and C(x3, y3, z3 ). Let AD, BE,and CF be the medians of ΔABC, where the co-ordinate of , and are (5, 7,11), (0, 8, 5) and (2, 3, −1) respectively.
Now,
(1) − (3) ⇒ x3 − x1 = 6
(2) + (4) ⇒ 2x3 = 6 ⇒ x3 = 3
(4) ⇒ x1 = −3
Also
Solving, y1 = 4, y2 = 2, y3 = 12.
And,
\(\frac{z_1+z_2}{2}=-1\\\frac{z_2+z_3}{2}=11\\\frac{z_1+z_3}{2}=5\)
Solving, z1= −7, z2 = 5, z3 = 17.
∴ Co-ordinates of vertices are A(−3, 4, −7), B(7, 2, 5) and C(3, 12, 17)
