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KCET2012MathematicsStraight Lines

The points (11,9),(2,1) and (2,-1) are the mid-points of the sides of the triangle. Then, the centroid is

Options

  1. A(-5,-3)
  2. B(5,-3)
  3. C(3,5)
  4. D(5,3)

Correct answer

D. (5,3)

Step-by-step solution

Let the vertices of a triangle be A (x₁, y₁ ) , B (x₂, y₂ ) and C (x₃, y₃ ) . Since, (11,9),(2,-1) and (2,1) are the mid-points of AB , BC and CA . array ll x₂+x₃ 2 =2, & y₂+y₃ 2 =-1 x₃+x₁ 2 =2, & y₃+y₁ 2 =1 array and x₁+x₂ 2 =11, y₁+y₂ 2 =9 x₂+x₃=4, x₃+x₁=4, x₁+x₂=22 2 (x₁+x₂+x₃ )=30 x₁+x₂+x₃=15 and y₁+y₃=+2, y₂+y₃=-2, y₁+y₂=18 2 (y₁+y₂+y₃ )=18 y₁+y₂+y₃=9 The centroid is = ( x₁+x₂+x₃ 3 , y₁+y₂+y₃ 3 ) = ( 15 3 , 9 3 )=(5,3)

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