To determine whether the dilation is an enlargement or a reduction, we need to compare the lengths of the segments \( AB \) and \( A'B' \) and find the scale factor between them.
- If \( A'B' \) is longer than \( AB \), then the dilation is an enlargement.
- If \( A'B' \) is shorter than \( AB \), then the dilation is a reduction.
Let's analyze the given options:
- If "AB is a reduction of A'B' by a scale factor of 1/2", this means \( A'B' \) is larger than \( AB \) by a factor of 2 (enlargement).
- If "A'B' is a reduction of AB by a scale factor of 1/2", it means \( AB \) is larger than \( A'B' \) by a factor of 2 (reduction).
- If "A'B' is an enlargement of AB by a scale factor of 2", it means \( A'B' \) is proportionally 2 times longer than \( AB\) (enlargement).
- If "AB is an enlargement of A'B' by a scale factor of 2", it means \( AB \) is proportionally 2 times longer than \( A'B' \) (enlargement).
Based on this information, we can conclude the type of dilation in terms of enlargement or reduction by evaluating the scale factors.
Without specific lengths or coordinates for points A, B, A', and B', I'm unable to definitively determine the correct option. However, if you have specific length information or coordinates, I can help you calculate the lengths and identify whether the dilation represents an enlargement or a reduction.
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