Explanation

(d)
Let $x_{1} = x,\ x_{2} = xr,\ x_{3} = {xr}^{2}$
$and\ y_{1} = y,\ y_{2} = yr,\ y_{3} = yr^{2}$
$\because x_{1},\ x_{2},\ x_{3}\ and\ y_{1},\ y_{2},\ y_{3}\$are in GP.
$\because\frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{y_{3} - y_{2}}{x_{3} - x_{2}} = \frac{y_{1} - y_{3}}{x_{1} - x_{3}}$
$\therefore\$The points ${(x}_{1},\ y_{1}),\ \left( x_{2},\ y_{2} \right)and\ (x_{3},\ y_{3})$ lies on a straight line.