Geometry

Question Analysis  

The focus is to determine the scale factor  for a dilation centered at , using the pre-image point  and its image .  

 

Key Concept Explanation  

For a dilation with center , the scale factor  is the ratio of the image's distance from the center to the pre-image's distance from the center:  

  

 must be consistent for both coordinates.  

 

Step-by-Step Solution  

1. Calculate horizontal distance ratio:  

Pre-image:   

Image:   

Scale factor:   

 

2. Verify with vertical distance ratio:  

Pre-image: