Q46 / 75 · JEE Main 2025 (7 Apr Shift 1) · Mathematics

Let ABC be the triangle such that the equations of lines $A B$ and $A C$ be $3 y-x=2$ and $x+y=2$, respectively, and the points B and C lie on x -axis. If $P$ is the orthocentre of the triangle $A B C$, then the area of the triangle PBC is equal to

A
4
B
10
C
8
Correct answer
D
6

Solution

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

Hence, the correct answer is option: 'D'.

Relevant Questions

In an equilateral triangle , let the vertex be at and the side be along the line . If the orthocentre of the triangle is , then is equal to:05 Apr, 2026 (M)Coordinate System
Let the vertex of a triangle be , and the mid-point of the side be . If the centroid of this triangle is and its circumcenter is , then is e04 Apr, 2026 (M)Coordinate System
Let , , be a point on the ellipse , be a point on the circle and be a point on the line such that the centroid of the triangle is . Then the04 Apr, 2026 (E)Coordinate System
Let be points on the two half-lines , at a distance of from their point of intersection . The line segment meets the angle bisector of the g04 Apr, 2026 (E)Coordinate System
Let the mid points of the sides of a triangle be , and . If its incentre is , then is equal to :02 Apr, 2026 (M)Coordinate System
Let ABC be an equilateral triangle with orthocenter at the origin and the side BC on the line . If the co-ordinates of the vertex A are , th28 Jan, 2026 (M)Coordinate System