Answer :

Given: The coordinates of the A and B of the triangle ABC are (3, -5, 7) and (-1, 7, -6) respectively. The centroid of the triangle is (1, 1, 1)


To find: the coordinates of vertex C


Formula used:


Centroid of triangle ABC whose vertices are A(x1, y1, z1), B(x2, y2, z2) and C(x3, y3, z3) is given by,



Here A(3, -5, 7) and B(-1, 7, -6)


Centroid of the triangle





On comparing:



2 + x3 = 3


x3 = 3 – 2


x3 = 1



2 + y3 = 3


y3 = 3 – 2


y3 = 1



1 + z3 = 3


z3 = 3 – 1


z3 = 2


Hence, coordinates of vertex C(1, 1, 2)


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