Write the coordinates of the third vertex of a triangle having centroid at the origin and two vertices at (3, -5, 7) and (3, 0, 1).

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)


7