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BITSAT2023MathematicsStraight LinesActual

If (-4,5) is one vertex and 7 x-y+8=0 is one diagonal of a square, then the equation of second diagonal is

Options

  1. Ax+3 y=21
  2. B2 x-3 y=7
  3. Cx+7 y=31
  4. D2 x+3 y=21

Correct answer

C. x+7 y=31

Step-by-step solution

One vertex of square is (-4,5) and equation of one diagonal is 7 x-y+8=0 Diagonal of a square are perpendicular and bisect each other Let the equation of the other diagonal be y=m x+c where m is the slope of the line and c is the y -intercept. Since this line passes through (-4,5) Since this line is at right angle to the line 7 x-y+8=0 or y=7 x+8 , having slope =7 , 7 m =-1 or m = -1 7 Putting this value of m in equation (i) we get 5=-4 ( -1 7 )+c or 5= 4 7 +c or c=5- 4 7 = 31 7 Hence equation of the other diagonal

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