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AP EAMCET202421 May 2024Morning ShiftMathematicsStraight LinesActual

If ( , ) is the orthocentre of the triangle with the vertices (2,2),(5,1),(4,4) , then + =

Options

  1. A6
  2. B5
  3. C5 2
  4. D7 2

Correct answer

A. 6

Step-by-step solution

A (2,2), B (5,1), C (4,4) Slope of A B= 1-2 5-2 = -1 3 Equation of CG aligned & y-4=3(x-4) & 3 x-y=8 aligned Slope of A C= 4-2 4-2 =1 Equation of BF y-1=-1(x-5) x+y=6 (ii) Solving (i) and (ii) we get (x, y)=( , )= ( 7 2 , 5 2 ) + = 12 2 =6

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