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

Let x2x1=x3x2=r  and  y2y1=y3y2=r⇒ x2 = x1r, x3 = x1r2, y2 = y1r and y3 = y1r2.We have,∆=x1y11x2y22x3y33=x1y11x1ry1r1x1r2y1r21=x1y11001-r001-r(Applying R3 → R3 – rR2 and R2 → R2 – rR1) = 0(∴ R2 and R3 are identical)Thus, (x1, y1), (x2, y2), (x3, y3) lie on a straight line