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AP EAMCET202124 Aug 2021Evening ShiftMathematicsStraight LinesActual

If the orthocenter and circumcenter of a triangle respectively are (3,-4,2) and (2,1,3) , then its centroid is

Options

  1. A( -7 3 , 6 3 , -4 3 )
  2. B( 7 3 , -6 3 , 4 3 )
  3. C( 7 3 , -6 3 , -4 3 )
  4. D( 7 3 , -2 3 , 8 3 )

Correct answer

D. ( 7 3 , -2 3 , 8 3 )

Step-by-step solution

Given, orthocentre and circumcentre of triangle are (3,-4,2) and (2,1,3) respectively We know that centroid of triangle is divide orthocentre and circumcentre in the ratio 2: 1 . Centroid of triangle is ( 3+2(2) 3 , -4+2(1) 3 , 2+2(3) 3 ) i.e., ( 7 3 , -2 3 , 8 3 )

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