To determine whether a dilation is an enlargement or a reduction, we need to look at the scale factor used in the dilation:
- If the scale factor is greater than 1, it is an enlargement.
- If the scale factor is between 0 and 1, it is a reduction.
Now let's analyze each option:
A. AB is an enlargement of A'B' by a scale factor of 2.
- Scale factor is 2 (>1), so this is an enlargement.
B. A'B is an enlargement of AB by a scale factor of 2.
- Scale factor is 2 (>1), so this is also an enlargement.
C. A'B is a reduction of AB by a scale factor of \(\frac{1}{2}\).
- Scale factor is \(\frac{1}{2}\) (<1), so this is a reduction.
D. AB is a reduction of A'B' by a scale factor of \(\frac{1}{2}\).
- Scale factor is \(\frac{1}{2}\) (<1), so this is a reduction.
In summary:
- Options A and B are enlargements.
- Options C and D are reductions.
So, if you are looking for a reduction, the correct answers are C and D. If you are looking for an enlargement, it would be A and B.
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