If $x_1, x_2, x_3$ as well as $y_1, y_2, y_3$ are in G.P. with the same common ratio, then the points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$

Let the common ratio be \(r\).

\[ x_1 = a, \; x_2 = ar, \; x_3 = ar^2 \] \[ y_1 = b, \; y_2 = br, \; y_3 = br^2 \]

So the points are \((a,b), \; (ar,br), \; (ar^2,br^2)\).

Slopes:

Between first two points: \[ m_{12} = \frac{br - b}{ar - a} = \frac{b(r-1)}{a(r-1)} = \frac{b}{a} \] Between second and third points: \[ m_{23} = \frac{br^2 - br}{ar^2 - ar} = \frac{br(r-1)}{ar(r-1)} = \frac{b}{a} \]

Since \(m_{12} = m_{23}\), the points are collinear.

Final Answer: The points \((x_1,y_1), (x_2,y_2), (x_3,y_3)\) are collinear.