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Question

Four vertices of a tetrahedron are (0,0,0),(4,0,0),(0,−8,0) and (0,0,12). Its centroid has the coordinates

A
(43,83,4)
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B
(2,4,6)
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C
(1,2,3)
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D
none of these
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Solution

The correct option is C (1,2,3)
If the vertices of tetrahedron are,(x1,y1,z1),(x2,y2,z2),(x3,y3,z3),(x4,y4,z4), then the centroid of tetrahedron is
(x1+x2+x3+x44,y1+y2+y3+y44,z1+z2+z3+z44)
Thus from the vertices given in the question, the centroid is
=(44,84,124)
=(1,2,3)

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