JEE Main: Orthocentre + Area Question Made Easy 💡
❓ Question Let A B C ABC be a triangle such that the equations of the lines A B : 3 y − x = 2 and A C : x + y = 2 AB:\ 3y-x=2 \quad \text{and} \quad AC:\ x+y=2 are given, and the points B and C lie on the x-axis . If P P is the orthocentre of triangle A B C ABC , then the area of triangle P B C PBC is equal to ? 🖼️ Question Image ✍️ Short Solution This problem combines: ✔ Finding points using line equations ✔ A key orthocentre shortcut when two vertices lie on the x-axis ✔ Computing area using base–height 🔹 Step 1 — Find coordinates of B and C Since B and C lie on the x-axis , set y = 0 y=0 . For point B (on line AB): 3 ( 0 ) − x = 2 ⇒ x = − 2 So, B ( − 2 , 0 ) For point C (on line AC): x + 0 = 2 ⇒ x = 2 So, C ( 2 , 0 ) 🔹 Step 2 — Find coordinates of A Point A is the intersection of lines A B AB and A C AC . Solve: 3 y − x = 2 ( 1 ) 3y-x=2 \quad (1) x + y = 2 ( 2 ) x+y=2 \quad (2) From (2): x = 2 − y x=2-y Substitu...