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AP EAMCET20226 Jul 2022Evening ShiftMathematicsThree Dimensional GeometryActual

Let the centroid of a triangle formed by the points A(4, x, 1), B(y,-5,2) and C(7,8,3) be G(3,5,2) and C G meet A B in F . Then, F=

Options

  1. A( 5 2 , 3 2 , 5 2 )
  2. B( 11 2 , 10,2 )
  3. C(1, 7 2 , 3 2 )
  4. D(10,12,5)

Correct answer

C. (1, 7 2 , 3 2 )

Step-by-step solution

Coordinate of G= ( 4+y+7 3 , x-5+8 3 , 1+2+3 3 ) aligned & (3,5,2)= ( 4+y+7 3 , x+3 3 , 2 ) & x+3 3 =5 x=12 & 11+y 3 =3 y=-2 aligned F is mid-point of A B aligned & =F ( 4+y 2 , x-5 2 , 1+2 2 ) & =F ( 4-2 2 , 12-5 2 , 3 2 )=F (1, 7 2 , 3 2 ) . aligned

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