MathematicsThe coordinates of P   which divides the line segment joining A 3,7  and B(9,4)   such that AP PB = 4 5   is:

The coordinates of P   which divides the line segment joining A 3,7  and B(9,4)   such that AP PB = 4 5   is:


  1. A
    P= 17 3 , 17 3  
  2. B
    P= 7 3 , 17 3  
  3. C
    P= 7 3 , 7 3  
  4. D
    P= 17 3 , 7 3   

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    Solution:

    Given that, the points are A 3,7  and B(9,4)   and AP PB = 4 5  .
    Hence, m = 4, n = 5.
    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 = 4, n = 5.
    ( x 1 , y 1 )=(3,7), ( x 2 , y 2 )=(9,4)  
    Substitute the known values in the formula,
    (x,y)=( 4(9)+5(3) 4+5 , 4(4)+5(7) 4+5 ) =( 36+15 9 , 16+35 9 ) =( 51 9 , 51 9 ) =( 17 3 , 17 3 )  
    The coordinate of P= 17 3 , 17 3  .
    Hence, option 1) is correct.
     
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