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In Δ P Q R , the equation of the internal angle bisector of angle Q is y = x and the equation of side P R is 3 x - y = 2 . If coordinates of P are 3,2 and 2 P Q = R Q , then the coordinates of Q are

Options

  1. A3,3
  2. B7,7
  3. C- 2 , - 2
  4. D5,5

Correct answer

B. 7,7

Step-by-step solution

Point of intersection of y = x & 3 x - y = 2 is S 1,1 Now, P S : S R = P R : R Q = 1 : 2 Hence, using section formula R = - 3 , - 1 Let, reflection of P about the line y = x is P ' ⇒ P ' = 2,3 which lies on the side Q R ⇒ equation of Q R is 4 x - 5 y + 7 = 0 Point of intersection of Q R & y = x is 7,7 = Q

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