If `x_1,x_2,x_3` as well as `y_1, y_2, y_3` are in G.P. with same common ratio, then prove that the points `(x_1, y_1),(x_2,y_2),a n d(x_3, y_3)` are collinear.

Explanation

To prove that the points \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\) are collinear, we will use the property of determinants. The points are collinear if the area of the triangle formed by them is zero, which can be determined using the determinant of the matrix formed by their coordinates.

### Step-by-Step Solution:

1. **Given Information**:
We know that \(x_1, x_2, x_3\) and \(y_1, y_2, y_3\) are in geometric progression (G.P.) with the same common ratio \(r\).

2. **Expressing the Terms**:
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