MathematicsIf M(9p−2,−q)   divides the line segment joining L(3p+1,−3)   and N(8p,5)   in the ratio 3:1  , find the values of p   and q  .

If M(9p2,q)   divides the line segment joining L(3p+1,3)   and N(8p,5)   in the ratio 3:1  , find the values of p   and q  .


  1. A
    p=2   and q=3  
  2. B
    p=1   and q=3  
  3. C
    p=1   and q=3  
  4. D
    p=1   and q=3   

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    Solution:

    Given that, M(9p2,q)   divides the line segment joining L(3p+1,3)   and N(8p,5)  .
    The ratio is 3:1  .
    If P(x, y) divides the line segment with the coordinates ( x 1 , y 1 ),( x 2 , y 2 )   in the ratio m:n internally, then the section formula is given by,
    P=( m x 2 +n x 1 m+n ),( m y 2 +n y 1 m+n )  .
    Here, m = 3, n = 1.
    ( x 1 , y 1 )=(3p+1,3), ( x 2 , y 2 )=(8p,5)  .
    Substituting the values in the formula, we get,
    (9p2,q)=( 3(8p)+1(3p+1) 3+1 , 3(5)+1(3) 3+1 )  
    Equating the x-coordinates, we get,
    9p2= 3 8p +1 3p+1 3+1 36p8=27p+1 27p=27   p=1  
    Equating the y-coordinates, we get,
    q= 3 5 +1 3 3+1 4q=153 4q=12   q=3   So, the coordinates is p,q = 1,3  .
    The value of  p=1   and q=3  .
    Hence, option 4) is correct.
     
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