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COMEDK202510 May 2025Evening ShiftMathematicsStraight LinesActual

The line AB passes through the point P(-4,3) and the portion of the line intercepted between the axes is divided internally in the ratio 5: 3 by the point P . Given that the point A lies on x -axis and B lies on y -axis, then the x intercept of the line is

Options

  1. A- 32 3
  2. B- 24 5
  3. C32 3
  4. D24 5

Correct answer

A. - 32 3

Step-by-step solution

Let the coordinates of point A on the x-axis be (a, 0) and the coordinates of point B on the y-axis be (0, b) . The point P(-4, 3) divides the segment AB internally in the ratio 5: 3 . Using the section formula, the coordinates of P are given by: P = ( 5(0) + 3(a) 5 + 3 , 5(b) + 3(0) 5 + 3 ) Equating the coordinates of P to (-4, 3) , we get: -4 = 3a 8 3a = -32 a = - 32 3 3 = 5b 8 5b = 24 b = 24 5 The x-intercept of the line is the x-coordinate of point A, which is a = - 32 3 . Answer: - 32 3

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