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AP EAMCET2016MathematicsThree Dimensional Geometry

If the plane 56 x+4 y+9 z=2016 meets the coordinate axes in A, B, C , then the centroid of the A B C is

Options

  1. A(12,168,224)
  2. B(12,168,112)
  3. C(12,168, 224 3 )
  4. D(12,-168, 224 3 )

Correct answer

C. (12,168, 224 3 )

Step-by-step solution

Given that equation of plane, aligned & 56 x+4 y+9 z=2016 & x 2016 56 + y 2016 4 + z 2016 9 =1 aligned Also given, this plane meets the coordinate axes at points A , B and C . Coordinate of A = ( 2016 56 , 0,0 ) Coordinate of B = (0, 2016 4 , 0 ) Coordinate of C = (0,0, 2016 9 ) Now, centroid of ABC G = ( 2016 56 3 , 2016 4 3 , 2016 9 3 )= (12,168, 224 3 )

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