Geometry

Question Analysis  

The main focus is to determine the scale factor of the dilation centered at the origin that transforms triangle to triangle . We need to use the relationship between corresponding coordinates of the pre - image and the image.

 

Key Concept Explanation  

For a dilation centered at the origin, if is a point in the pre - image and is the corresponding point in the image, then , where is the scale factor. A negative indicates a reflection across the origin, |k|>1 means enlargement, and |k|<1 means reduction.

 

Step-by-Step Solution

1. Select a pair of corresponding points: Let's choose point and its corresponding point .

2. Calculate the scale factor using the - coordinates:

Using the formula