Sure! Let's analyze the given options and determine which statement is correct regarding the dilation of a triangle by a scale factor of \( n = \frac{1}{3} \).
Dilation involves resizing a figure by a scale factor. The scale factor \( n \) will determine whether the figure enlarges, reduces, or stays the same size:
- If \( n > 1 \), the figure enlarges.
- If \( 0 < n < 1 \), the figure reduces.
- If \( n = 1 \), the figure remains the same size.
- If \( n < 0 \), the figure also involves a reflection in addition to resizing, but this case is less common in standard dilation problems.
Given the scale factor \( n = \frac{1}{3} \):
- \( \frac{1}{3} \) is greater than 0 but less than 1 (\( 0 < \frac{1}{3} < 1 \)).
- Therefore, this dilation results in a reduction of the triangle.
Now let's verify which option correctly describes this situation:
1. It is a reduction because \( n > 1 \).
- This statement is incorrect because \( n = \frac{1}{3} \) is not greater than 1.
2. It is a reduction because \( 0 < n < 1 \).
- This statement is correct because \( n = \frac{1}{3} \) satisfies the condition \( 0 < \frac{1}{3} < 1 \).
3. It is an enlargement because \( n > 1 \).
- This statement is incorrect because \( n = \frac{1}{3} \) is not greater than 1.
4. It is an enlargement because \( 0 > n > 1 \).
- This statement is incorrect because \( n = \frac{1}{3} \) is not in the range \( 0 > n > 1 \).
Thus, the correct statement regarding the dilation of the triangle is:
It is a reduction because [tex]\( 0 < n < 1 \)[/tex].
