MathematicsIf points (a,0),(0,b)   and (1,1)   are collinear, then find the value of 1 a + 1 b  .

If points (a,0),(0,b)   and (1,1)   are collinear, then find the value of 1 a + 1 b  .


  1. A
    1
  2. B
    2
  3. C
    3
  4. D
    4 

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    Solution:

    Given that, the points (a,0),(0,b),(1,1)   are collinear.
    We have to find the value of 1 a + 1 b  .
    If the points ( x 1 , y 1 ),( x 2 , y 2 ),( x 3 , y 3 )   are collinear, then 1 2 x 1 y 2 y 3 + x 2 y 3 y 1 + x 3 y 1 y 2 =0  .
    Now,
    ( x 1 , y 1 )=(a,0) ( x 2 , y 2 )=(0,b) ( x 3 , y 3 )=(1,1)  
    Substitute the values to check if the points (a,0),(0,b),(1,1)   are collinear:
    1 2 a b1 +0 10 +1 0b =0 aba+00+0b=0 abab=0 ab=a+b  
      1= a+b ab a ab + b ab =1 1 a + 1 b =1  
    The value of 1 a + 1 b =1.  
    Hence, option 1) is correct.
     
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