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JEE Main202524 Jan 2025Morning ShiftMathematicsStraight LinesActual

Let the lines 3 x-4 y- =0,8 x-11 y-33=0 , and 2 x-3 y+ =0 be concurrent. If the image of the point (1,2) in the line 2 x-3 y+ =0 is ( 57 13 , -40 13 ) , then | | is equal to

Options

  1. A84
  2. B113
  3. C91
  4. D101

Correct answer

C. 91

Step-by-step solution

aligned & PM = QM & So, M ( 57 13 +1 2 , -40 13 +2 2 ) & = ( 35 13 , -7 13 ) aligned M lies on the line gathered 2 x-3 y+ =0 2 ( 35 13 )-3 ( -7 13 )+ =0 =- 70 13 + 21 13 = -91 13 =-7 | array ccc 3 & -4 & - 8 & -11 & -33 2 & 3 & array |=0 gathered aligned & 3(-11 -99)+4(8 +66)- (-24+22)=0 & 33 -297+32 +264+24 -22 =0 & - +2 -33=0 & =-7 & -(-7)+2 -33=0 & 2 =26 & =13 & | |=|13 (-7)| & =91 aligned

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