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Points A = (0,5) and B = (10,13) are joined to form line segment AB.  If point P = (x,y) divides AB in the ratio 3:1 externally, then what is x + y?

 Jan 9, 2020
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The point divides the line into two segments in ratio of 3:1    the point is thus 3/4 from the end.     (3 +1 =4)  

    there are two points (depending on which end of the line you start at ) which will divide the line this way....

I will assume the point P is furthest away from A

 

the x coordinate will be    0  +   (10 - 0 ) x 3/4 = 7.5

the y coordinate will be  5 +  (13-5)   x 3/4  = 11

 

x+y = 18.5     Sorry....this was for INTERNAL  ratio division

 

For EXTERNAL  ratio of 3:1    m = 3 n = 1

Formula: Y={[(mx2-nx1)/(m-n)],[(my2-ny1)/(m-n)]}

 

3(10)-(1)(0)   /   ((3-1) = xp =  15

3(13)-1(5)     / (3-1)      = yp = 17                        

 

Thanx geno for spotting my error !

 
 Jan 9, 2020
edited by ElectricPavlov  Jan 10, 2020

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