Question

if (2,3,4) is centroid of the tetrahedron for which (2,3,-1),(3,0,-2),(-1,4,3) are the three vertices then the fourth vertex is​

Answer 1

The fourth vertex will be (4,5,16)

Answer 2

Answer:

Centroid (G)= (2,3,4)

A= (2,3,-1) = (x1, y1, z1)

B= (3,0,-2) = (x2, y2, z2)

C= (-1,4,3) = (x3, y3, z3)

D= (x4, y4, z4)

Formula (To remember)

G=( x1+x2+x3+x4/4 , y1+y2+y3+y4/4 , z1+z2+z3+z4/4)

G=(2,3,4)= ((2+3+(-1)+x4)/4 , (3+0+4+y4)/4 , ((-1)+(-2)+3+z4)/4)

(2,3,4)= ((5-1+x4)/4, (7+y4)/4, (-1-2+3+z4)/4)

(2,3,4)= ((4+x4)/4, (7+y4)/4, z4/4)

Equating

1. (4+x4)/4=2

4+x4=2x4

x4=8-4

x4=4

2. (7+y4)/4=3

7+y4=12

y4=12-7

y4=5

3. x4/4=4

x4=4x4

x4=16

D=(x4,y4,z4)

 =(4,5,16)