The equations of two sides AB and AC of a triangle A B C are 4 x+y=14 and 3 x-2 y=5 , respectively. The point (2,-4/3 ) divides the third side BC internally in the ratio 2: 1 . The equation of the side BC is :

Mathematics · Straight lines

JEE Main 2024 — 8 April, Shift 1 — Question 13

The equations of two sides AB and AC of $a$ triangle $A B C$ are $4 x+y=14$ and $3 x-2 y=5$ , respectively. The point $\left(2,-\frac{4}{3}\right)$ divides the third side BC internally in the ratio $2: 1$ . The equation of the side BC is :

Option A:
$x-6 y-10=0$
Option B:
$x-3 y-6=0$
Option C:
$x+3 y+2=0$
Correct
Option D:
$x+6 y+6=0$

Answer: C

Step-by-step solution

$\frac{2 \mathrm{x}_{2}+\mathrm{x}_{1}}{3}=2, \frac{2\left(\frac{3 \mathrm{x}_{2}-5}{2}\right)+\left(14-4 \mathrm{x}_{1}\right)}{3}=\frac{-4}{3}$

$2 x_{2}+x_{1}=6,3 x_{2}-4 x_{1}=-13$

$\mathrm{x}_{2}=1, \mathrm{x}_{1}=4$

So, $\mathrm{C}(1,-1), \mathrm{B}(4,-2)$

$\mathrm{m}=\frac{-1}{3}$ Equation of $B C: y+1=\frac{-1}{3}(x-1)$

$\begin{aligned} & 3 y+3=-x+1 \end{aligned}$

$x+3 y+2=0$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 8 April, Shift 1
Subject: Mathematics
Chapter: Straight lines
Topic: Various forms of lines

If the orthocentre of the triangle formed by the lines 2 x+3 y-1=0, x+2 y-1=0 and ax+ by-1=0 , is the centroid of another triangle, whose…

Answer: C

Step-by-step solution

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