If x1,x2,x3 as well as y1,y2,y3 are in G.P. with same common ratio, then the points P(x1,y1),Q(x2,y2)  andR(x3,y3) .

Let x1=a,x2=ar andx3=ar2;y1=b,y2=br andy3=br2 . Nowy2−y1x2−x1=br2−brar2−ar=baTherefore, slope of PQ is equal to slope of QR. Hence, points P, Q, R are collinear.