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NTA Abhyas JEE Main2020MathematicsStraight LinesPractice

The point P ( 2 , 1 ) is shifted through a distance of 3 2 units measured perpendicular to the line x - y = 1 in the direction of decreasing ordinates, to reach at Q . The image of Q with respect to te line y + x = 1 is

Options

  1. A3 , - 4
  2. B- 3 , 2
  3. C0 , - 1
  4. D5 , - 2

Correct answer

A. 3 , - 4

Step-by-step solution

P Q = 3 2 ⇒ x Q = 2 + 3 2 ⋅ 1 2 = 5 and y Q = 1 - 3 2 ⋅ 1 2 = - 2 ⇒ Q ≡ 5 , - 2 Distance of Q from the line x + y = 1 is 5 - 2 - 1 2 = 2 ⇒ Q R = 2 2 ⇒ x R = 5 - 2 2 ⋅ 1 2 = 3 and y R = - 2 - 2 2 ⋅ 1 2 = - 4 Thus, R ≡ 3 , - 4

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