Geometry

Question Analysis  

The main focus is to determine if dilating collinear points preserves their collinearity, leveraging the core property of dilations.  

Key Concept Explanation  

Collinearity in Dilations: Dilations preserve collinearity. Any set of collinear points remains collinear after dilation, as the transformation maps straight lines to straight lines.  

Step-by-Step Solution  

1. Original Collinearity: Points , ,  lie on a straight line.  

2. Dilation Effect: A dilation with  scales all coordinates but does not alter the linear relationship between points. The dilated points , ,  will lie on the same straight line as the original points, but with distances scaled by

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