Geometry

Question Analysis

The main focus is to determine the range of the scale factor  for the given dilation, which requires comparing the positions of corresponding points in the original and dilated figures.

Key Concept Explanation

For a dilation centered at the origin:

If k>1, the dilation is an enlargement, meaning the dilated figure is larger than the original.

If k = 1, the figure remains unchanged.

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

Step - by - Step Solution

1. Let's take a point, say . Suppose  has coordinates  and  has coordinates .

2. Calculate the scale factor using the

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