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AP EAMCET201921 Apr 2019Morning ShiftMathematicsStraight LinesActual

Two vertices of a triangle are (5,-1) and (-2,3) . If the origin is the orthocentre of this triangle, then the coordinates of the third vertex of that triangle are

Options

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

Correct answer

C. (-4,-7)

Step-by-step solution

Slope of B C slope of A D=-1 3+1 -2-5 k h =-1 k h 4 -7 =-1 Slope of A B slope of C F=-1 aligned & M_ A B M_ C F =-1 array l M_ C F 3-0 -2-0 = -3 2 array & M_ A B -3 2 =-1 M_ A B = 2 3 aligned Equation of A B array rlrl & & y+1 & = 2 3 (x-5) & 3 y+3 & =2 x-10 & 2 x-3 y & =13 array A(h, k) lie on line A B From Eqs. (i) and (ii), we get h=-4, k=-7 Hence, third vertex of the triangle =(-4,-7)

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