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AP EAMCET202125 Aug 2021Morning ShiftMathematicsThree Dimensional GeometryActual

If the origin is the centroid of the triangle for which (-2,3,4) and (3,-1,5) are two vertices, then the third vertex is

Options

  1. A(1,2,9)
  2. B(-1,-2,9)
  3. C(1,-2,-9)
  4. D(-1,-2,-9)

Correct answer

D. (-1,-2,-9)

Step-by-step solution

Let the vertices of triangle be A(x, y, z), B(-2,3,4), C(3,-1,5) Centroid of A B C is aligned ( x-2+3 3 , y+3-1 3 . & ., z+4+5 3 ) & = ( x+1 3 , y+2 3 , 2+9 3 ) aligned Given that centroid of A B C is origin aligned & x+1 3 =0 x=-1 & y+2 3 =0 y=-2 & z+9 3 =0 z=-9 aligned Third vertex (-1,-2,-9) .

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