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COMEDK202510 May 2025Morning ShiftMathematicsStraight LinesActual

If two vertices of a triangle are (3,-2) and (-2,3) and its orthocentre is (-6,1) . Then the difference between ordinate and abscissa of the third vertex of the triangle is

Options

  1. A2
  2. B-5
  3. C7
  4. D5

Correct answer

C. 7

Step-by-step solution

Let the vertices of the triangle be A(3, -2) , B(-2, 3) , and C(x, y) . The orthocentre H is given as (-6, 1) . The slope of BC is m_ BC = y - 3 x - (-2) = y - 3 x + 2 . Since AH BC , the slope of AH is m_ AH = 1 - (-2) -6 - 3 = 3 -9 = - 1 3 . The condition m_ AH m_ BC = -1 implies (- 1 3 ) ( y - 3 x + 2 ) = -1 , which simplifies to y - 3 x + 2 = 3 , so y - 3 = 3x + 6 , or 3x - y + 9 = 0 . The slope of AC is m_ AC = y - (-2) x - 3 = y + 2 x - 3 . Since BH AC , the slope of BH is m_ BH = 1 - 3 -6 - (-2) = -2 -4 = 1

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