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JEE Main 20257 AprilMorning Shift
Exam
JEE Main
Year
2025
Date
7 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2025 · 7 April · Morning Shift · Mathematics · Straight Lines

Let ABC be the triangle such that the equations of lines A B and A...

Let ABC be the triangle such that the equations of lines ABA B and ACA C be 3y−x=23 y-x=2 and x+y=2x+y=2, respectively, and the points B and C lie on x -axis. If PP is the orthocentre of the triangle ABCA B C, then the area of the triangle PBC is equal to

Options

  1. A4
  2. B10
  3. C8
  4. D6

Correct answer

D. 6

Step-by-step solution

 Equation of Altitude AP:x=1 Equation of Altitude BP:y−0=1(x+2)⇒x=1x−y+2=0P(1,3) Area of △PBC=12×4×3=6\begin{aligned} & \text{ Equation of Altitude } \mathrm{AP}: \mathrm{x}=1 \\ & \text{ Equation of Altitude } \mathrm{BP}: \mathrm{y}-0=1(\mathrm{x}+2) \\ & \Rightarrow \mathrm{x}=1 & \\ & \mathrm{x}-\mathrm{y}+2=0 \\ & \mathrm{P}(1,3) \\ & \text{ Area of } \triangle \mathrm{PBC}=\frac{1}{2} \times 4 \times 3=6\end{aligned}
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