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AP EAMCET20224 Jul 2022Evening ShiftMathematicsStraight LinesActual

The equation of perpendicular bisectors of sides A B and A C of a ∆ A B C are x - y + 5 = 0 and x + 2 y = 0 respectively. If the coordinates of vertex A are 1 , - 2 , then equation of B C is

Options

  1. A14 x + 23 y - 40 = 0
  2. B14 x - 23 y + 40 = 0
  3. C23 x + 14 y - 40 = 0
  4. D23 x - 14 y + 40 = 0

Correct answer

A. 14 x + 23 y - 40 = 0

Step-by-step solution

Let B ( x 1 ,   x 1 ) and C ( x 2 ,   y 2 ) be two vertices and P x 1 + 1 2 , y 1 - 2 2   being mid point of AB lies on its perpendicular bisector PN having equation x - y + 5 = 0 ∴ x 1 + 1 2 - y 1 - 2 2 = - 5 ⇒   x 1 - y 1 = - 13 ...(i) Also, P N is perpendicular to A B . ∴   y 1 + 2 x 1 - 1 × 1 = - 1 (Slopes of AB and PN satistfy the condition for slopes of perpendicular lines , Product of slopes= -1 ) ⇒   x 1 + y 1 = - 1 ...(ii) On solving Eqs. (i) and (

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