The centroid of a triangle ABC is at the point (1, 1, 1). If the coordinates of
A and B are (3, -5, 7) and (-1, 7, -6) respectively, find the coordinates of
the point C.
Let G be the centroid of △ABC
Given : G ≡ (1, 1, 1)
Let C ≡ (x, y, z)
Then, 1 = 3−1+x3
⇒3=3−1+x
⇒3=2+x⇒x=1
and 1 = −5+7+y3
⇒3=2+y
⇒y=1
and 1 = 7−6+z3
⇒3=1+z
⇒ z = 2