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:
\(\frac{6+x_3}{3}\) = 0
⇒ 6 + x3 = 0
⇒ x3 = –6
\(\frac{-5+y_3}{3}\) = 0
⇒ -5 + y3 = 0
⇒ y3 = 5
\(\frac{8+z_3}{3}\) = 0
⇒ 8 + z3 = 0
⇒ z3 = – 8
Hence, coordinates of vertex C(-6, 5, -8)
