Step-by-step Solution:

Let \[ x_1 = a, \quad x_2 = ar, \quad x_3 = ar^2 \] and \[ y_1 = b, \quad y_2 = br, \quad y_3 = br^2 \] Now, calculating the slope between the first two points: \[ \frac{y_2 - y_1}{x_2 - x_1} = \frac{br - b}{ar - a} \] Factor out common terms: \[ = \frac{b(r - 1)}{a(r - 1)} \] \[ = \frac{b}{a} \] Similarly, for the second and third points: \[ \frac{y_3 - y_2}{x_3 - x_2} = \frac{br^2 - br}{ar^2 - ar} \] Factor out common terms: \[ = \frac{br(r - 1)}{ar(r - 1)} \] \[ = \frac{b}{a} \] Since both slopes are equal, the three points are collinear. Thus, the points lie on the same line, proving collinearity. \[ \boxed{\text{Collinear}} \]