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AP EAMCET202418 May 2024Morning ShiftMathematicsStraight LinesActual

If the lines 3 x+y-4=0, x- y+10=0, x+2 y+4= 0 and 3 x+y+k=0 represent the sides of a square, then (k+4)^2=

Options

  1. A-256
  2. B-512
  3. C-128
  4. D-1024

Correct answer

B. -512

Step-by-step solution

Since, m_ AB =-3, m_ BC = 1 m_ AB m_ BC =-1 -3 =-1 =3 aligned & and m_ AD = - 2 m_ AD m_ AB =-1 (-3) ( - 2 )=-1 & = -2 3 aligned Now, AB = |10+4| 1^2+(-3)^2 = 16 10 and BC = |k+4| 1+9 = k+4 10 Since, AB = BC 16 10 = k+4 10 k=12 Now, (k+4)^2=3 ( -2 3 ) 256=-512

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