Geometry

Question Analysis

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

 

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 value indicates a reflection across the origin, |k|>1 means the figure is enlarged, and |k|<1 means it's reduced.

 

Step-by-Step Solution

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

2. Calculate the scale factor using the - coordinates:

Using the formula