Mathematics · 2022
JEE Main · 28 June 2022, Shift 2 · Q12
Let a triangle be bounded by the lines L_1: 2 x+5 y=10; L_2:-4 x+3 y=12 and the line L_3, which passes through the point P(2, 3), intersects L_2 at A…
Let a triangle be bounded by the lines $\displaystyle \mathrm{L}_1: 2 x+5 y=10 ; \mathrm{L}_2:-4 x+3 y=12$ and the line $\displaystyle \mathrm{L}_3$, which passes through the point P$\displaystyle (2, 3)$, intersects $\displaystyle \mathrm{L}_2$ at A and $\displaystyle \mathrm{L}_1$ at B. If the point P divides the line-segment AB, internally in the ratio $\displaystyle 1$ : $\displaystyle 3$, then the area of the triangle is equal to :
Official answer
(2)
$\displaystyle \frac{132}{13}$
More from Straight Lines
- The equations of the sides AB, BC and CA of a triangle ABC are 2 x+y=0, x+p y=15 a and x-y=3 respectively. If its orthocentre is (2, a),-1/2<a<2,…2022
- Consider the lines x(3 λ+1)+y(7 λ+2)=17 λ+5, λ being a parameter, all passing through a point P. One of these lines (say L ) is farthest from the…2025
- Let A B C be an isosceles triangle in which A is at (-1,0), ∠ A=(2 π)/3, A B=A C and B is on the positve x -axis. If B C=4 √3 and the line B C…2024
- If the line, 2 x-y+3=0 is at a distance 1/(√5) and 2/(√5) from the lines 4 x-2 y+α=0 and 6 x-3 y+β=0, respectively, then the sum of all possible…2020
- Let ABC be a triangle formed by the lines 7 x-6 y+3=0, x+2 y-31=0 and 9 x-2 y-19=0. Let the point (h, k) be the image of the centroid of Δ ABC in the…2025
- Let tan α, tan β and tan γ; α, β, γ ≠ ((2 n-1) π)/2, n ∈ N be the slopes of three line segments OA, OB and OC, respectively, where O is origin. If…2021
- One side of a square lies along the line x-3 y+1=0 and its one vertex is (1,4). If (a, b) and (c, d) are its two vertices on the line x-3 y+1=0, then…2021
- If the point (α, (7 √3)/3) lies on the curve traced by the mid-points of the line segments of the lines x cos θ+y sin θ=7, θ ∈(0, (π)/2) between the…2023
JEE Main 2022 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.