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AP EAMCET2013MathematicsStraight Lines

If 2 x+3 y=5 is the perpendicular bisector of the line segment joining the points A (1, 1 3 ) and B , then B is equal to

Options

  1. A( 21 13 , 49 39 )
  2. B( 17 13 , 31 39 )
  3. C( 7 13 , 49 39 )
  4. D( 21 13 , 31 39 )

Correct answer

D. ( 21 13 , 31 39 )

Step-by-step solution

Let l₁ 2 x+3 y=5 Since, line A B I₁ Slope of l₁ is array r m₁ say = -2 3 Slope of A B= -1 (-2 / 3) = 3 2 array Equation of line A B is array cc & (y- 1 3 )= 3 2 (x-1) & 3 x-2 y= 7 3 array Equation of line I₁ is 2 x+3 y=5 From Eqs. (i) and (ii), we get array rl 13 x & =17 x & x= 17 13 array From Eq. (i), we get 3 y=5- 34 13 y= 65-34 13 3 = 31 39 So, mid-point P ( 17 13 , 31 39 ) Coordinate of point B aligned & = ( 17 13 2-1, 31 39 2- 1 3 ) & = ( 34-13 13 , 62-13 39 )= ( 21 13 , 49 39 ) aligned

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