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KCET2007MathematicsStraight Lines

A B C is triangle, G is the centroid, D is the mid-point of B C . If A=(2,3) and G=(7,5) , then the point D is

Options

  1. A( 9 2 , 4 )
  2. B( 19 2 , 6 )
  3. C( 11 2 , 11 2 )
  4. D(8, 13 2 )

Correct answer

B. ( 19 2 , 6 )

Step-by-step solution

Since, D is the mid-point of B C . So, coordinate of B C are ( x₂+x₃ 2 , y₂+y₃ 2 ) Given, G(7,5) is the centroid of A B C . 7= 2+x₂+x₃ 3 and 5= 3+y₂+y₃ 3 x₂+x₃=21-2 and y₂+y₃=15-3 array ll & x₂+x₃=19 and & y₂+y₃=12 array x₂+x₃ 2 = 19 2 and y₂+y₃ 2 =6 Coordinate of D are ( 19 2 , 6 ) .

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