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Question and Answer

If the vertices of a triangle are \((-1,6,-4),(2,1,1)\) and \((5,-1,0)\) then the centroid of the triangle is

(A) \((6,6,-3)\)
(B) \((2,2,-1)\)
(C) \(\left ( 3,3,-\displaystyle \frac{3}{2} \right )\)
(D) none of these

Answer

Answer: B
the centroid of the triangle is
\((\dfrac {x_1+x_2+x_3}{3},\dfrac{y_1+y_2+y_3}{3},\dfrac{z_1+z_2+z_3}{3})\)

Thus by substituting the vertices we get
\(=(\dfrac{-1+2+5}{3},\dfrac{6+1-1}{3},\dfrac{-4+1+0}{3})\)

\(=(\dfrac{6}{3},\dfrac{6}{3},\dfrac{-3}{3})\)
\(\therefore\)the centroid of the triangle is \((2,2,-1)\)

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