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AP EAMCET202316 May 2023Evening ShiftMathematicsStraight LinesActual

The circumcentre of the triangle with vertices (-2,3) , (2,-1),(4,0) is

Options

  1. A( 3 2 , 5 2 )
  2. B( 3 2 , -5 2 )
  3. C( -3 2 , 5 2 )
  4. D( -3 2 , -5 2 )

Correct answer

A. ( 3 2 , 5 2 )

Step-by-step solution

Given the vertices (-2,3),(2,-1), &(4,0) Let O(x, y) be the circumcentre of the triangle. Let ABC be the triangle. Then OA = OB = OC OA ^2 OB ^2 ( x +2)^2+( y -3)^2=( x -2)^2+( y +1)^2 aligned & x-y=-1 ... (i) & and O C^2=O B^2 & (x-4)^2+(y-0)^2=(x-2)^2+(y+1)^2 & 4 x+2 y=11 ... (ii) aligned By solving (i) & (ii), we get x= 3 2 , y= 5 2

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