To determine whether the dilation is an enlargement or a reduction, we need to look at the scale factors mentioned for each case:
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AB is a reduction of A′B′ by a scale factor of \( \frac{1}{2} \): This means that A′B′ is larger than AB, so it indicates a reduction (AB is smaller).
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A′B′ is a reduction of AB by a scale factor of \( \frac{1}{2} \): This means AB is larger than A′B′, indicating a reduction (A′B′ is smaller).
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AB is an enlargement of A′B′ by a scale factor of \( 2 \): This means AB is larger than A′B′, indicating an enlargement (AB is bigger).
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A′B′ is an enlargement of AB by a scale factor of \( 2 \): This means A′B′ is larger than AB, indicating an enlargement (A′B′ is bigger).
In summary:
- A reduction occurs if the scale factor is less than 1.
- An enlargement occurs if the scale factor is greater than 1.
Based on these principles:
- The statements regarding reductions (1 and 2) are correct about one being a reduction of the other.
- Conversely, statements (3 and 4) indicate enlargements.
To summarize:
- If the scale factor is \( \frac{1}{2} \), this implies a reduction.
- If the scale factor is \( 2 \), this implies an enlargement.
Thus, you can conclude from the cases presented.