The co-ordinates of the vertices of the given tetrahedron are (1,2,3), (5,8,6),(14,15,18) and (0,0,0). Find the co-ordinates of the centroid of the tetrahedron?

(5,7,6)

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(5,6.25,6.75)

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(7,5,6)

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(6.67, 8.34, 9)

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Solution

The correct option is B (5,6.25,6.75)
$For the coordinates of the centroid of the tetrahedron x = \frac{1 + 5 + 14 + 0}{4} = 5 y = \frac{2 + 8 + 15 + 0}{4} = 6.25 z = \frac{3 + 6 + 18 + 0}{4} = 6.75 (x, y, z) = (5, 6.25, 6.75)$

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The co-ordinates of the vertices of the given tetrahedron are (1,2,3), (5,8,6),(14,15,18) and (0,0,0). Find the co-ordinates of the centroid of the tetrahedron?

The correct option is B (5,6.25,6.75)For the coordinates of the centroid of the tetrahedronx =1+5+14+04 =5y =2+8+15+04 =6.25z =3+6+18+04 =6.75(x,y,z) =(5,6.25,6.75)

The correct option is B (5,6.25,6.75)
$For the coordinates of the centroid of the tetrahedron x = \frac{1 + 5 + 14 + 0}{4} = 5 y = \frac{2 + 8 + 15 + 0}{4} = 6.25 z = \frac{3 + 6 + 18 + 0}{4} = 6.75 (x, y, z) = (5, 6.25, 6.75)$