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AP EAMCET202119 Aug 2021Evening ShiftMathematicsStraight LinesActual

If A ( 4 , 7 ) , B ( - 7 , 8 ) and C ( 1 , 2 ) are the vertices of ∆ A B C , then the equation of perpendicular bisector of the side A B is

Options

  1. Ax − 11 y − 24 = 0
  2. B11 x + y + 24 = 0
  3. C11 x − y + 24 = 0
  4. D11 x + y − 24 = 0

Correct answer

C. 11 x − y + 24 = 0

Step-by-step solution

The slope of the side A B is 8 - 7 - 7 - 4 = - 1 11 Hence, the slope of the line which is perpendicular to A B is 1 - - 1 11 = 11 (Say m ) Now, say, point D is the mid-point of the line A B , Hence, the co ordinate of point D is - 3 2 ,   15 2 . Now, the equation of perpendicular bisector will be the equation of the line which passes through point D and perpendicular to the line A B is y - 15 2 = m x - - 3 2   ⇒ y - 15 2 = 11 x - - 3 2   ⇒ y - 15 2 = 11 x + 3 2 ⇒ 11 x - y + 24 = 0

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