To determine whether a dilation is an enlargement or a reduction, we look at the scale factor:
- If the scale factor is greater than 1, it is an enlargement.
- If the scale factor is less than 1 but greater than 0, it is a reduction.
Let's analyze the statements provided:
-
AB is a reduction of A′B′ by a scale factor of \( \frac{1}{2} \).
- Here, \( \frac{1}{2} < 1 \), indicating that AB is smaller than A′B′. Thus, it is a reduction.
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A′B′ is a reduction of AB by a scale factor of \( \frac{1}{2} \).
- This statement is inverse to the first and also means \( A′B′ \) is smaller than \( AB \), confirming it is also a reduction.
-
A′B′ is an enlargement of AB by a scale factor of 2.
- Here, the scale factor of 2 is greater than 1, indicating that A′B′ is larger than AB. Thus, this represents an enlargement.
-
AB is an enlargement of A′B′ by a scale factor of 2.
- This statement is the inverse of the third, implying that AB is larger than A′B′, confirming it is also an enlargement.
From this analysis, we can conclude:
- Statements referring to a scale factor of \( \frac{1}{2} \) indicate reductions.
- Statements referring to a scale factor of 2 indicate enlargements.
In summary:
- A reduction occurs when the scale factor is \( \frac{1}{2} \) (as given in the first and second statements).
- An enlargement occurs when the scale factor is 2 (as stated in the third and fourth statements).