To solve this problem, we need to understand how the scale factor [tex]\( n \)[/tex] affects the dilation of a geometric figure, such as a triangle.
The scale factor [tex]\( n \)[/tex] determines whether the dilation results in an enlargement or a reduction:
1. If [tex]\( n > 1 \)[/tex], the dilation is an enlargement. This means the image is larger than the original figure.
2. If [tex]\( 0 < n < 1 \)[/tex], the dilation is a reduction. This means the image is smaller than the original figure.
3. If [tex]\( n = 1 \)[/tex], there is no change in size; the image is congruent to the original figure.
4. If [tex]\( n < 0 \)[/tex], the dilation not only changes the size but also reflects the image across the origin, which isn't typically addressed as a simple enlargement or reduction.
Given [tex]\( n = \frac{1}{3} \)[/tex]:
1. We notice that [tex]\( n \)[/tex] is a positive fraction, specifically [tex]\( 0 < \frac{1}{3} < 1 \)[/tex].
2. Since [tex]\( \frac{1}{3} \)[/tex] falls within the range of [tex]\( 0 < n < 1 \)[/tex], this indicates that the dilation results in a reduction.
Thus, the correct statement regarding the dilation is:
"It is a reduction because [tex]\( 0 < n < 1 \)[/tex]."
