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P,Q,R is a point on the side of the triangle AB, BC and CA respectively. if P, Q and R divides the sides AB, BC and CA in the ratio m:1. Find the centroid of the triangle ABC.
Dear Chanchal ,
let A = (a1 ,a2) ; B =(b1, b2) ; C =(c1, c2)
p = (mb1+a1/m+1 , mb2+a2/m+1) , Q = (mc1+b1/m+1 , mc2+b2/m+1) , R = (ma1+c1/m+1 , ma2+c2/m+1)
centroid = p+Q+R/3
= (m(a1+b1+c1)+(a1+b1+c1)/(m+1)) /3, m(a2+b2+c2)+(a2+b2+c2)/(m+1)/3
= (a1+b1+c1)/3 ,(a2+b2+c2)/3
i.e same as the triangle ABC .
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