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If two vertices of a triangle are (5,-1) and (-2,3) and its orthocentre is at (0,0) , then the third vertex is

Options

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

Correct answer

B. (-4,-7)

Step-by-step solution

Let the third vertex of A B C be (a, b) . Orthocentre =H(0,0) Let A(5,-1) and B(-2,3) be other two vertices of A B C . Now, (Slope of A H) ( Slope of B C)=-1 aligned & ( -1-0 5-0 ) ( b-3 a+2 )=-1 & b-3=5(a+2) aligned Similarly, ( Slope of B H) ( Slope of A C)=-1 aligned & - ( 3 2 ) ( b+1 a-5 )=-1 & 3 b+3=2 a-10 & 3 b-2 a+13=0 aligned On solving equation (1) and (2) we get a=-4, b=-7 Hence, third vertex is (-4,-7) .

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