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Solution


Q.

Let ABC be the triangle such that the equation of lines AB and AC be 3y – x = 2 and x + y = 2, respectively, and the points B and C lie on x-axis. If P is the orthocentre of the triangle ABC, then the area of the triangle PBC is equal to          [2025]
1 10  
2 4  
3 8  
4 6  

Ans.

(4)

Equation of Altitude AP, which is perpendicular to BC is given by

x = 1          ... (i)

Equation of Altitude BP, which is perpendicular to AC is given by

y – 0 = 1(x + 2) ⇒ x – y + 2 = 0          ... (ii)

Hence, P≡(1, 3)          [From (i) and (ii)]

∴  Area of △PBC=12×4×3=6 sq. units