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COMEDK2020MathematicsStraight Lines

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

Correct answer

A. ( 19 2 , 6 )

Step-by-step solution

We know that, centroid divides median in the ratio 2:1. aligned (7,5) &= ( 2 x+2 2+1 , 2 y+3 2+1 ) (7,5) &= ( 2 x+2 3 , 2 y+3 3 ) 2 x+2 3 &=7 and 2 y+3 3 =5 x &= 19 2 and y=6 D & is ( 19 2 , 6 ) . aligned

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