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MHT CET202311 May 2023Evening ShiftMathematicsStraight LinesActual

If the vertices of a triangle are (-2,3),(6,-1) and (4,3) , then the co-ordinates of the circumcentre of the triangle are

Options

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

Correct answer

D. (1,-1)

Step-by-step solution

Here, A (-2,3), B (6,-1), C (4,3) are the vertices of ABC . Let F be the circumcentre of ABC . Let FD and FE be the perpendicular bisectors of the sides BC and AC respectively. D and E are the midpoints of side BC and AC respectively. array ll & D ( 6+4 2 , -1+3 2 ) & D=(5,1) & and E ( -2+4 2 , 3+3 2 ) array E =(1,3) Now, slope of B C= 3-(-1) 4-6 = 4 -2 =-2 Slope of FD = 1 2 [ FD BC ] Since FD passes through (5,1) and has slope 1 2 , equation of FD is aligned & y-1= 1 2 (x-5) & 2(y-1)=x-5 & 2 y-2=x-5 & x-2 y-3=0 al

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