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AP EAMCET201823 Apr 2018Morning ShiftMathematicsStraight LinesActual

The circumcentre of the triangle with vertices at (-2,3),(1,-2) and (2,1) is

Options

  1. A( 6 7 , 2 7 )
  2. B(- 6 7 , 2 7 )
  3. C( 6 7 ,- 2 7 )
  4. D(- 6 7 ,- 2 7 )

Correct answer

B. (- 6 7 , 2 7 )

Step-by-step solution

Let vertices of A B C is A(-2,3), B(1,-2) and C(2,1) Circumcentre of triangle is a point where perpendicular bisector of sides meet. So, D E is perpendicular bisector of B C . So, D E is perpendicular bisector of B C . D is mid-point of B C , so coordinate of D ( 1+2 2 , -2+1 2 )=D ( 3 2 , -1 2 ) Slope of B C= 1+2 2-1 =3 Since D E B C , slope of D E=- 1 3 Now, equation of D E is aligned (y+ 1 2 ) & = -1 3 (x- 3 2 ) y+ 1 2 & =- 1 3 x+ 1 2 3 y=-x aligned Now, F E is perpendicular bisector of A B Coordinate of F ( -1

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