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Viany Lohani Grade: 11
        


Ar = (Xr,Yr), r=1,2,3………,n is a set of n points. P1 divides A1A2 in the ratio 1:1, P2 divides P1A3 in th ratio 1:2, P3 divides P2A4 in the ratio 1:3 and so on . Pn-1 divides Pn-2An in the ratio 1:n-1, Find The Co-ordinates of Pn-1?


6 years ago

Answers : (1)

Askiitians_Expert Yagyadutt
askIITians Faculty
74 Points
										

Hii vinay !


 


This is very nice question ....Try to understand this -


 


 


A1     P1         A2            P2           A3             P3            A4             P4               A5                  .........Pn-1.......  An


 


(x1,y1)          (x2,y2)                 (x3,y3)                                                                                                      (xn,yn) 


 


P1   divides A1 A2 in 1:1


 


so P1 = [(x1 +x2)/2 ,(y1+y2)/2 ]


 


P2 divides P1A3 is 1 : 2 ...


 


so P2 =  [2P1 + A3 ]/3   =   [ (x1+x2+x3)/3 , (y1+y2+y3)/3 ]


 


Similarly in P3  you will get   [ (x1+x2+x3+x4)/4 , (y1 + y2 + y3 +y4)/4]


 


And thus Pn-1 = [ (x1+x2+x3........+xn)/n , )y1+y2+y3........+yn)/n ]


 


 


Note : simply use the section formula which means if any point (h,k) divide (p,q) and (r,s) in ration a:1


 


(p.q)...............a.........(h,k)...................1............(r,s)


 


Then  h  = (a.r + p )/(a+1)   k = ( as + q)/(a+1) 


 


 


With regards


 


yagya


askiitians_expert

6 years ago
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