Geometry

Question Analysis  

The main focus is to determine the scale factor for a dilation centered at the origin, using the coordinates of the original point and its image .  

 

Key Concept Explanation  

Dilation formula centered at the origin: For a point , the image after dilation by scale factor is . A negative indicates reflection across the origin.  

 

Step-by-Step Solution  

1. Set up equations for the - and -coordinates using the dilation formula:  

For the -coordinate:  

For the -coordinate:  

2. Solve for in either equation:  

From the -coordinate:

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