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COMEDK2025MathematicsStraight LinesActual

The inclination of a straight line passing through the point (-3,6) and the midpoint of the line joining the points (4,-5) and (-2,9) is

Options

  1. A6
  2. B3
  3. C3 4
  4. D4

Correct answer

C. 3 4

Step-by-step solution

Let the given points be A = (4, -5) and B = (-2, 9) . The midpoint M of the line segment AB is calculated as: M = ( 4 + (-2) 2 , -5 + 9 2 ) = ( 2 2 , 4 2 ) = (1, 2) The line passes through the point P = (-3, 6) and M = (1, 2) . The slope m of this line is given by: m = y₂ - y₁ x₂ - x₁ = 2 - 6 1 - (-3) = -4 1 + 3 = -4 4 = -1 The inclination of the line is the angle such that = m . Thus, = -1 . Since = -1 , the principal value of in the interval [0, ) is = - 4 = 3 4 . Answer: 3 4

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