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AP EAMCET20228 Jul 2022Evening ShiftMathematicsStraight LinesActual

If the coordinates of the vertices of a A B C are A(7,6,4), B(5,4,6), C(3,2,0) and the bisector of B A C meets the side B C at D , then the coordinates of D are

Options

  1. A( 13 3 , 10 3 , 4 )
  2. B( 11 3 , 8 3 , 2 )
  3. C(9,8,6)
  4. D(7,5,3)

Correct answer

A. ( 13 3 , 10 3 , 4 )

Step-by-step solution

A D is the angle bisector of A . A B A C = B D C D Now, aligned & A B= 4+4+4 =2 3 & A C= 16+16+16 =4 3 aligned B D C D = 2 3 4 3 = 1 2 D divides B C in the ratio 1: 2 internally. D ( 3+10 3 , 8+2 3 , 12+0 3 ) ( 13 3 , 10 3 , 4 )

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