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JEE Main2012MathematicsStraight LinesActual

Let L be the line y=2 x , in the two dimensional plane. Statement 1: The image of the point (0,1) in L is the point ( 4 5 , 3 5 ) Statement 2: The points (0,1) and ( 4 5 , 3 5 ) lie on opposite sides of the line 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 ) be the image of (0,1) with respect to the line 2 x-y=0 then aligned & x₁ 2 = y₁-1 -1 = -4(0)+2(1) 5 & x₁= 4 5 , y₁= 3 5 aligned Thus, statement- 1 is true. Also, statement-2 is true and correct explanation for statement-1.

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