Geometry

Question Analysis  

The main focus is to determine if dilation can make non-collinear points collinear, based on the property that dilations preserve (but do not create) collinearity.  

Key Concept Explanation  

Collinearity and Dilation: Dilations preserve collinearity for existing straight lines, but they cannot make non-collinear points collinear. If points are not on a straight line before dilation, they will not be collinear after dilation, regardless of the scale factor.  

Step-by-Step Solution  

1. Given Non-Collinearity: Points , ,  are not collinear.  

2. Apply Dilation Property: Dilations map straight lines to straight lines, but they do not transform non-linear configurations into linear ones. Since the original points are not collinear, the dilated points , ,

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