If the centroid of the tetrahedron is 0,−1,52 and three vertices are (−2,3,4),(3,−4,2),(2,−5,1) then the fourth vertex is

-2+3+2+x4,3-4-5+y,4,4+2+1+z4=0,-1,52⇒x,y,z=-3,2,3

If the centroid of the tetrahedron is 0,−1,52 and three vertices are (−2,3,4),(3,−4,2),(2,−5,1) then the fourth vertex is

-2+3+2+x4,3-4-5+y,4,4+2+1+z4=0,-1,52⇒x,y,z=-3,2,3

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$If the centroid of the tetrahedron is (0, - 1, \frac{5}{2}) and three vertices are (- 2, 3, 4), (3, - 4, 2), (2, - 5, 1) then$ $the fourth vertex is$

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$(0 . - 1, 5)$

$(1, 0.5)$

$(- 3, 2, 3)$

$(5 . - 1, 0)$

answer is A.

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Detailed Solution

$(\frac{- 2 + 3 + 2 + x}{4}, \frac{3 - 4 - 5 + y,}{4}, \frac{4 + 2 + 1 + z}{4}) = (0, - 1, \frac{5}{2})$ $\Rightarrow (x, y, z) = (- 3, 2, 3)$

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If the centroid of the tetrahedron is 0,−1,52 and three vertices are (−2,3,4),(3,−4,2),(2,−5,1) then the fourth vertex is

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$If the centroid of the tetrahedron is (0, - 1, \frac{5}{2}) and three vertices are (- 2, 3, 4), (3, - 4, 2), (2, - 5, 1) then$ $the fourth vertex is$