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JEE Main201910 Jan 2019Morning ShiftMathematicsStraight LinesActual

If the line 3 x + 4 y - 24 = 0 intersects the x -axis is at the point A and the y -axis at the point B , then the incentre of the triangle O A B , where O is the origin, is:

Options

  1. A4 , 4
  2. B3 , 4
  3. C4 , 3
  4. D2 , 2

Correct answer

D. 2 , 2

Step-by-step solution

The x intercept of the line 3 x + 4 y - 24 = 0 can be obtained by putting y = 0 i.e. 3 x - 24 = 0 ⇒ x = 8 Hence, the point A is 8 ,   0 . Now, the y intercept of the line 3 x + 4 y - 24 = 0 can be obtained by putting x = 0 i.e. 4 y - 24 = 0 ⇒ y = 6 Hence, the point B is 0 ,   6 . In ∆ O A B , we have O A = b = 8 ,   O B = a = 6 and A B = c = 8 - 0 2 + 0 - 6 2 = 64 + 36 = 10 units. And, we know that the co-ordinates of incentre I of a triangle with vertices x 1 ,   y 1 ,  

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