Answer :

Given: The coordinates of the A and B of the triangle ABC are (3, -5, 7) and (3, 0, 1) respectively. The centroid of the triangle is (0, 0, 0)


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(3, 0, 1)


Centroid of the triangle





On comparing:



6 + x3 = 0


x3 = –6



-5 + y3 = 0


y3 = 5



8 + z3 = 0


z3 = –8


Hence, coordinates of vertex C(-6, 5, -8)


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