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COMEDK2012MathematicsStraight Lines

If a vertex of traingle is (3,3) and the mid-points of two sides through this vertex are (2, 3 2 ) and (4, 3 2 ) , then the centroid of the triangle is given by

Options

  1. A(1,3)
  2. B(3,0)
  3. C(3,1)
  4. D(0,3)

Correct answer

C. (3,1)

Step-by-step solution

Let the vertices of A B C are A(3,3), B (x₁, y₁ ) and C (x₂, y₂ ) . Now, x₁+3 2 =2 and y₁+3 2 = 3 2 x₁+3=4 and y₁+3=3x₁=1 and y₁=0 So, B (1,0) and x₂+3 2 =4 and y₂+3 2 = 3 2 x₂+3=8 and y₂+3=3x₂=5 and y₂=0C (5,0) Hence, centroid = ( 3+1+5 3 , 3+0+0 3 ) = ( 9 3 , 3 3 )=(3,1)

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