The Line Segment Joining A(6, 3) To B(–1, –4) Is Doubled In Length By Having Its Length Added To Each End. Find The Coordinates Of The New Ends.

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Question

The line segment joining A(6, 3) to B(–1, –4) is doubled in length by having its length added to each end. Find the coordinates of the new ends.

Solution

Correct option is

 

Let P and Q be the required new ends. 

Let the coordinates of P be (x1y1)      

Given          AB = 2AP

  

i.e., A divides BP internally in the ratio 2 : 1. 

  

  

    

  

Also let coordinates of Q be (x2y2

Given AB = 2BQ    

  

i.e.B divides AQ internally in the ratio 2 : 1 

  

  

  

  

Alternative Method : 

  

  

  

 P divides AB externally in the ratio 1 : 3 

   

  

 

Also      AB = 2BQ

  

  

 Q divides AB externally in the ratio 3 : 1 

    

  

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Testing

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