Let's analyze the dilation scale factor [tex]\( n = \frac{1}{3} \)[/tex].
To determine the effect of the dilation, it’s important to understand the meaning of the scale factor [tex]\( n \)[/tex].
1. Reduction (shrinkage):
- If the scale factor [tex]\( n \)[/tex] is between [tex]\( 0 \)[/tex] and [tex]\( 1 \)[/tex], i.e., [tex]\( 0 < n < 1 \)[/tex], the size of the image will be smaller than the original. This is known as a reduction.
2. Enlargement:
- If the scale factor [tex]\( n \)[/tex] is greater than [tex]\( 1 \)[/tex], i.e., [tex]\( n > 1 \)[/tex], the size of the image will be larger than the original. This is known as an enlargement.
Let's place our given scale factor into these two categories:
- For [tex]\( n = \frac{1}{3} \)[/tex]:
- It falls within the range [tex]\( 0 < n < 1 \)[/tex]. Thus, this qualifies as a reduction because the image size will be smaller than the original.
Now, review the given statements in the question:
1. It is a reduction because [tex]\( n > 1 \)[/tex].
- Incorrect, because for [tex]\( n = \frac{1}{3} \)[/tex], [tex]\( n < 1 \)[/tex].
2. It is a reduction because [tex]\( 0 < n < 1 \)[/tex].
- Correct, because the scale factor [tex]\( n = \frac{1}{3} \)[/tex] lies within the range [tex]\( 0 < n < 1 \)[/tex].
3. It is an enlargement because [tex]\( n > 1 \)[/tex].
- Incorrect, the scale factor [tex]\( n \)[/tex] is less than 1, not greater.
4. It is an enlargement because [tex]\( 0 > n > 1 \)[/tex].
- Incorrect and doesn't make logical sense, as there's no range where [tex]\( 0 > n > 1 \)[/tex].
Thus, the true statement regarding the dilation is:
It is a reduction because [tex]\( 0 < n < 1 \)[/tex]. (which corresponds to the second statement)
Therefore, the correct choice is statement number 2.
