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If x₁, x₂, x₃ and y₁, y₂, y₃ each form geometric progressions with the same common ratio, then the points (x₁, y₁), (x₂, y₂), and (x₃, y₃)

1. form the vertices of a triangle
2. are collinear
3. lie on an ellipse
4. lie on a circle

Correct answer: are collinear

Solution

The points (x₁, y₁), (x₂, y₂), and (x₃, y₃) are collinear because both sets of coordinates form geometric progressions with the same common ratio, which implies that the ratios of the differences between corresponding x and y coordinates are constant, satisfying the condition for collinearity.

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