Question

Find the centroid of the triangle whose vertices are (3,6,5),(6,2,7) and (3,1,9).

Answer 1

The centroid of the triangle = "G(4, 2, 7)".

Step-by-step explanation:

Given, the vertices of triangle are (3,6,5), (6,2,7) and (3,1,9).

Let the centroid of the triangle  =G(x, y, z)

$(x_{1} = 3, y_{1} = 6, z_{1} = 5), (x_{2} = 6, y_{2} = 2, z_{2} = 7) and (x_{3} = 3, y_{3} = 1, z_{3} = 9).$

∴ $x =\frac{x_{1} + x_{2} + x_{3} }{3}$

⇒ $x =\frac{3 + 6 + 3 }{3}$

⇒ $x =\frac{12 }{3}$

⇒ x = 4

$y =\frac{y_{1} + y_{2} + y_{3} }{3}$

⇒ $x =\frac{3 + 2 + 1 }{3}$

⇒ $x =\frac{6}{3}$

⇒ y = 2

And

$z =\frac{z_{1} + z_{2} + z_{3} }{3}$

⇒ $x =\frac{5 + 7 + 9}{3}$

⇒ $x =\frac{21}{3}$

⇒ z = 7

∴ The centroid of the triangle is G(4, 2, 7).

Hence, the centroid of the triangle = G(4, 2, 7).

Answer 2

hope, it will help you