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STATEMENT-1 : The centroid of a tetrahed...

STATEMENT-1 : The centroid of a tetrahedron with vertices (0, 0,0), (4, 0, 0), (0, -8, 0), (0, 0, 12)is (1, -2, 3).
and
STATEMENT-2 : The centroid of a triangle with vertices `(x_(1), y_(1), z_(1)), (x_(2), y_(2), z_(2)) and (x_(3), y_(3), z_(3))` is
`((x_(1)+x_(2)+x_(3))/3, (y_(1)+y_(2)+y_(3))/3, (z_(1)+z_(2)+z_(3))/3)`

A

Statement-1 is True, Statement-2 is true, Statement- is a correct explanation for Statement -1

B

Statement-1 is True, Statement-2 is true, Statement- is NOT a correct explanation for Statement -1

C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False, Statement-2 is true

Text Solution

Verified by Experts

The correct Answer is:
B
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Show that the coordinates off the centroid of the triangle with vertices A(x_(1),y_(1),z_(1)),B(x_(2),y_(2),z_(2)) and (x_(3),y_(3),z_(3)) are ((x_(1)+x_(2)+x_(3))/(3),(y_(1)+y_(2)+y_(3))/(3),(z_(1)+z_(2)+z_(3))/(3))

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