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MHT CET202615 April 2026Morning ShiftMathematicsStraight LinesActual

If a triangle ABC has vertices A(1,-6), B(2,-3) and C(3,-2) , then the coordinates of its orthocenter are....

Options

  1. A(-6, 1)
  2. B(6, 1)
  3. C(-2, 3)
  4. D(3, 2)

Correct answer

A. (-6, 1)

Step-by-step solution

Let the vertices of the triangle be A(1, -6) , B(2, -3) , and C(3, -2) . The slope of the side BC is m_ BC = -2 - (-3) 3 - 2 = 1 . The altitude from A to BC is perpendicular to BC , so its slope is -1 . The equation of the altitude from A(1, -6) is: y - (-6) = -1(x - 1) x + y = -5 ... (i) The slope of the side AC is m_ AC = -2 - (-6) 3 - 1 = 4 2 = 2 . The altitude from B to AC is perpendicular to AC , so its slope is - 1 2 . The equation of the altitude from B(2, -3) is: y - (-3) = - 1 2 (x - 2) 2y + 6 = -x + 2 x +

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