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MHT CET20244 May 2024Morning ShiftMathematicsThree Dimensional GeometryActual

Let a, b R . If the mirror image of the point p ( a , 6,9) w.r.t. line x-3 7 = y-2 5 = z-1 -9 is (20, b,-a-9) , then |a+b| is equal to

Options

  1. A88
  2. B86
  3. C90
  4. D84

Correct answer

A. 88

Step-by-step solution

Note that mid-point of the line joining points (a, 6,9) and (20, b,-a-9) lies on the given line. The midpoint is ( a +20 2 , 6+ b 2 , 9- a -9 2 ) Substituting this point in the equation of the given line, we get array ll & a+20 2 -3 7 = 6+b 2 -2 5 = -a 2 -1 -9 & a+14 14 = a+2 18 & a=-56 & -56+4 14 = 2+b 10 & b=-32 & |a+b|=88 array

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