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JEE Main 201219 MayOnline
Exam
JEE Main
Year
2012
Date
19 May
Mode
Online
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2012 · 19 May · Online · Mathematics · Straight Lines

Let L be the line y=2 x , in the two dimensional plane. Statement...

Let LL be the line y=2xy=2 x, in the two dimensional plane. Statement 1: The image of the point (0,1)(0,1) in LL is the point \left(\frac{4}{5}, \frac{3}{5}\right)Statement2:ThepointsStatement 2: The points(0,1)and(45,35)and \left(\frac{4}{5}, \frac{3}{5}\right) lie on opposite sides of the line L\mathrm{L} and are at equal distance from it.

Options

  1. AStatement 1 is true, Statement 2 is false.
  2. BStatement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.
  3. CStatement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
  4. DStatement 1 is false, Statement 2 is true.

Correct answer

C. Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.

Step-by-step solution

Statement - 1 Let P′(x1,y1)beP^{\prime} \left(x_1, y_1\right) be the image of(0,1)withrespecttothelinewith respect to the line2 x-y=0thenthenx12=y1−1−1=−4(0)+2(1)5⇒x1=45,y1=35\begin{aligned} \frac{x_1}{2}=\frac{y_1-1}{-1}=\frac{-4(0)+2(1)}{5}\\ & \Rightarrow x_1=\frac{4}{5}, y_1=\frac{3}{5} \end{aligned}$$ Thus, statement- 1 is true. Also, statement-2 is true and correct explanation for statement-1.
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