Question

Find the third vertex of a triangle whose centroid is origine and two vertices are (2,4,6) and (0,-2,-5)

Answer 1

Okay, this is an easy question.

So the centroid of the triangle when the vertices are known will be $(x_1 + x_2 + x_3)/3$

take the coordinates of the third point as (x,y,z)

As the coordinates of the origin ( centroid ) are (0,0,0)

• (x+2+0)/3 = 0 ⇒x=-2
• (y+4-2)/3 = 0 ⇒ y= -2

(z+0-5)/3 = 0 ⇒ z= -1

So the answer is (-2,-2,-1)

Thank you.