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NTA Abhyas JEE Main2020MathematicsStraight LinesPractice

Let the coordinates of two points P and Q be 1,2 and 7,5 respectively. The line P Q is rotated through 315 ° in clockwise direction about the point of trisection of P Q which is nearer to Q . The equation of the line in the new position is

Options

  1. A2 x - y - 6 = 0
  2. Bx - y - 1 = 0
  3. C3 x - y - 11 = 0
  4. D3 x - y - 9 = 0

Correct answer

C. 3 x - y - 11 = 0

Step-by-step solution

Point of trisection nearer to Q is 5,4 . After rotation, the slope of the line is tan ⁡ θ 1 = tan ⁡ 45 ° + tan ⁡ θ 2 1 - tan ⁡ 45 ° tan ⁡ θ 2 = 1 + 1 2 1 - 1 2 = 3 (where, tan ⁡ θ 2 is the slope of A B ) Equation of the required line is y - 4 = 3 x - 5 ⇒ 3 x - y - 11 = 0

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