Given that the triangle is dilated by a scale factor of [tex]\( n = \frac{1}{3} \)[/tex], let's analyze what this scaling factor implies.
1. Understanding the Scale Factor:
- The scale factor [tex]\( n = \frac{1}{3} \)[/tex] is a positive number.
- To determine the kind of transformation (reduction or enlargement), we examine the value of [tex]\( n \)[/tex].
2. Evaluating the Scale Factor:
- If the scale factor is [tex]\( 0 < n < 1 \)[/tex], the image after dilation is smaller than the original figure. This is referred to as a reduction.
- If the scale factor is [tex]\( n > 1 \)[/tex], the image after dilation is larger than the original figure. This is known as an enlargement.
3. Applying the Scale Factor [tex]\( n = \frac{1}{3} \)[/tex]:
- Since [tex]\( \frac{1}{3} \)[/tex] is a positive number between 0 and 1, specifically [tex]\( 0 < \frac{1}{3} < 1 \)[/tex].
4. Conclusion:
- Because the scale factor [tex]\( n = \frac{1}{3} \)[/tex] meets the condition [tex]\( 0 < n < 1 \)[/tex], the dilation results in a reduction of the original triangle.
Therefore, the correct statement is:
"It is a reduction because [tex]\( 0 < n < 1 \)[/tex]."
