MathematicsIf the coordinates of the points P   and Q   are 2,5  and  8,6   respectively, find the coordinates of L   such that PL LQ = 2 5  .

If the coordinates of the points P   and Q   are 2,5  and  8,6   respectively, find the coordinates of L   such that PL LQ = 2 5  .


  1. A
    L= 6,37  
  2. B
    L= 26 7 , 37 7  
  3. C
    L= 6 7 , 37 7  
  4. D
    L= 26 7 , 37 7   

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    Solution:

    Given that, the coordinates of the points P   and Q   are 2,5  and  8,6  .
    PL LQ = 2 5  .
    Hence, m = 2, n = 5.
    If L(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,
    L=( m x 2 +n x 1 m+n ),( m y 2 +n y 1 m+n )  .
    Here, m = 2, n = 5.
    ( x 1 , y 1 )=(2,5), ( x 2 , y 2 )=(8,6)  
    L(x,y)=( 2(8)+5(2) 2+5 , 2(6)+5(5) 2+5 ) =( 16+10 7 , 12+25 7 ) =( 26 7 , 37 7 )  
    The coordinate of L is 26 7 , 37 7  .
    Hence, option 4) is correct.
     
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