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MHT CET202313 May 2023Morning ShiftMathematicsThree Dimensional GeometryActual

If A(1,4,2) and C(5,-7,1) are two vertices of triangle ABC and G ( 4 3 , 0, -2 3 ) is centroid of the triangle ABC , then the mid point of side BC is

Options

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

Correct answer

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

Step-by-step solution

Let B (x₁, y₁, z ₁ ) Co-ordinates of centroid gathered ( 1+x₁+5 3 , 4+y₁-7 3 , 2+ z ₁+1 3 ) ( 4 3 , 0, -2 3 ) ( 6+x₁ 3 , y₁-3 3 , 3+ z ₁ 3 ) x₁=-2, y₁=3, z ₁=-5 B (-2,3,-5) Midpoint side BC = ( -2+5 2 , 3-7 2 , -5+1 2 ) = ( 3 2 ,-2,-2 ) gathered

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