Verified Solution • 2025–26 Session moderate

QJEEM24Ma8644: JEE Main 2024 Mathematics - Class 11 JEEM24Ma8644 Solution: Let be the point of intersection of the lines and be the point…

Let A\mathrm{A} be the point of intersection of the lines 3x+2y=14,5x−y=63 x+2 y=14,5 x-y=6 and B\mathrm{B} be the point of intersection of the lines 4x+3y=8,6x+y=54 x+3 y=8,6 x+y=5 . The distance of the point P(5,−2)P(5,-2) from the line AB\mathrm{AB} is

Multiple Choice Options

  • A 6
  • B 132\frac{13}{2}
  • C 8
  • D 52\frac{5}{2}

Step-by-Step Verified Solution

Solving lines L1(3x+2y=14)\mathrm{L}_1(3 \mathrm{x}+2 \mathrm{y}=14) and L2(5x−y=6)\mathrm{L}_2(5 \mathrm{x}-\mathrm{y}=6) to get A(2,4)\mathrm{A}(2,4) and solving lines L3(4x+3y=8)\mathrm{L}_3(4 \mathrm{x}+3 \mathrm{y}=8) and L4(6x+y=5)\mathrm{L}_4(6 \mathrm{x}+\mathrm{y}=5) to get B(12,2)\mathrm{B}\left(\frac{1}{2}, 2\right) .

Finding Eqn. of AB:4x−3y+4=0\mathrm{AB}: 4 \mathrm{x}-3 \mathrm{y}+4=0

Calculate distance PM

⇒∣4(5)−3(−2)+45∣=6\Rightarrow\left|\frac{4(5)-3(-2)+4}{5}\right|=6

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