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AP EAMCET201920 Apr 2019Morning ShiftMathematicsStraight LinesActual

The equation of the perpendicular bisectors of the sides (A B ) and (A C ) of a ( A B C ) are (x-y+5=0 ) and (x+2 y+5=0 ), respectively. If (A ) is ((1,-2) ), then the equation of the straight line (B C ) is

Options

  1. A(14 x+23 y-40=0 )
  2. B(12 x+17 y-28=0 )
  3. C(14 x-29 y-30=0 )
  4. D(7 x-12 y+15=0 )

Correct answer

A. (14 x+23 y-40=0 )

Step-by-step solution

The point (B (x₁, y₁ ) ) is the reflection of point (A ) w.r.t. line (x-y+5=0 ), so ( aligned x₁-1 1 & = y₁+2 -1 & =-2 1+2+5 2 =-8 x₁ & =-7, y₁=6 aligned ) so, (B(-7,6) ) Similarly point (C (x₂, y₂ ) ) is the reflection of point (A ) w.r.t., line (x+2 y=0 ), so ( x₂-1 1 = y₂+2 2 =-2 1-4 5 = 6 5 ) ( x₂= 11 5 ) and (y₂= 2 5 ) So, (C ( 11 5 , 2 5 ) ). Now, equation of line (B C ) is ( array cc & y-6= 6- 2 5 -7- 11 5 (x+7) & y-6= 28 -46 (x+7) & y-6= -14 23 (x+7) & 14 x+23 y=138-98 & 14 x+23 y-40=0 array ) Hence, option

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