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JEE Main 201412 AprilOnline
Exam
JEE Main
Year
2014
Date
12 April
Mode
Online
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2014 · 12 April · Online · Mathematics · Straight Lines

If a line intercepted between the coordinate axes is trisected at a...

If a line intercepted between the coordinate axes is trisected at a point A(4,3)\mathrm{A}(4,3), which is nearer to xx-axis, then its equation is:If a line intercepted between the coordinate axes is trisected at a point A(4,3) , which is nearer to x -axis, then itsIf a line intercepted between the coordinate axes is trisected at a point A(4,3) , which is nearer to x -axis, then its

Options

  1. A4x−3y=74 x-3 y=7
  2. B3x+2y=183 \mathrm{x}+2 \mathrm{y}=18
  3. C3x+8y=363 x+8 y=36
  4. Dx+3y=13x+3 y=13

Correct answer

B. 3x+2y=183 \mathrm{x}+2 \mathrm{y}=18

Step-by-step solution

If a line intercepted between the coordinate axes is trisected at a point A(4,3) , which is nearer to x -axis, then its
 A divides CB in  \text{ A divides } \mathrm{CB} \text{\text{ in } }2: 1 ⇒4=(1×0+2×a1+2)=2a3⇒a=6⇒ coordinate of B is B (6,0)3=(1×b+2×01+2)=b3⇒b=9 and C(0,9)\begin{aligned}&\Rightarrow 4=\left(\frac{1 \times 0+2 \times a}{1+2}\right)=\frac{2 a}{3}\\ &\Rightarrow a=6 \Rightarrow \text{ coordinate of B is B }(6,0) \\ &3=\left(\frac{1 \times b+2 \times 0}{1+2}\right)=\frac{b}{3}\\ &\Rightarrow b=9 \text{ and } \mathrm{C}(0,9) \end{aligned}Slope of line passing through (6,0),(0,9)(6,0),(0,9) slope, m=9−6=−32m=\frac{9}{-6}=-\frac{3}{2} Equation of line y−0=−32(x−6)y-0=\frac{-3}{2}(x-6)2y=−3x+183x+2y=18\begin{aligned}&2 y=-3 x+18 \\ &3 x+2 y=18 \end{aligned}$
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