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BITSAT2010MathematicsStraight LinesActual

The reflection of the point ((4,-13) ) in the line (5 x+y+6=0 ), is

Options

  1. A((-1,-14) )
  2. B((3,4) )
  3. C((1,2) )
  4. D((-4,13) )

Correct answer

A. ((-1,-14) )

Step-by-step solution

Let ( Q (a, b) ) be the reflection of ( P (4,-13) ) in the line (5 x+y+6=0 ) Then the mid-point (R ( a+4 2 , b-13 2 ) ) lies on ( aligned & 5 x+y+6=0 & 5 ( a+4 2 )+ b-13 2 +6=0 & 5 a+b+19=0 ...(i) aligned ) Also ( PQ ) is perpendicular to (5 x+y+6=0 ) Therefore ( b+13 a-4 (- 5 1 )=-1 ) ( a-5 b-69=0 ...(ii) ) Solving (i) and (ii), we get (a=-1, b=-14 )

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