Let Asub$1,$ Asub$2,...,$Asubn be n points in a plane. For each Asubisub$1,$ Asubisub$2,...$ Asubisubk we call the centroid of Asubisub$1,$ Asubisub$2,...$ Asubisubk a point Gsubisub$1,...$Gsubisubk such that the line segment OGsubisub$1...$OGsubisubk $=($OAsubisub$1+....+$OAsubisubk$)/($k$).$ SHow that the centroid of Asub$1,$ Asub$2,...,$ Asubk, the centroid of Asubk$+1,$ Asubk$+2,...,$Asubn and the centroid of all the points Asub$1,$ Asub$2,....,$ Asubn are on a line.