Geometry

Question Analysis

The main focus is to determine the range of the scale factor  for the given dilation by comparing the coordinates of corresponding points in the original and dilated figures.

Key Concept Explanation

For a dilation centered at the origin:

When k>1, it is an enlargement, meaning the dilated figure is larger than the original.

When k = 1, the figure remains unchanged.

When 0 < k < 1, it is a reduction, and the dilated figure is smaller than the original.

Step - by - Step Solution

1. Consider point  and its image .

2. Calculate the scale factor using the  - coordinates (since  for both). The formula for the scale factor

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