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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?
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
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