MathematicsFrom the following choices, find the ratio in which line segment joining −1,3  and  4,−7   is divided by 2,−3  .

From the following choices, find the ratio in which line segment joining 1,3  and  4,7   is divided by 2,3  .


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

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    Solution:

    Given that, 1,3  and  4,7   is divided by P(2, -3).
    We have to find the ratio.
    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 )  .
    P(x,y)=P(2,3) ( x 1 , y 1 )=(1,3), ( x 2 , y 2 )=(4,7)  
    Let the ratio be k:1.
    Substitute the values in the formula,
    (2,3)=( k(4)+1(1) k+1 , k(7)+1(3) k+1 ) (2,3)=( 4k1 k+1 , 7k+3 k+1 )  
    Equating x-coordinate, we get,
    4k1 k+1 =2 4k1=2k+2 4k2k=2+1 2k=3 k= 3 2  
    The ratio is 3:2  .
    Hence, option 4) is correct.
     
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