Answer :
To determine which statement is true regarding the dilation of a triangle by a scale factor of \( n = \frac{1}{3} \), let's analyze the properties of dilation and the given scale factor.
Step-by-Step Solution:
1. Understanding Scale Factor:
- In geometry, a dilation is a transformation that produces an image that is the same shape as the original figure, but is a different size.
- The scale factor (\( n \)) determines whether the dilation is an enlargement or a reduction.
2. Comparison of Scale Factor:
- If \( n > 1 \), the dilation is an enlargement (the figure becomes larger).
- If \( 0 < n < 1 \), the dilation is a reduction (the figure becomes smaller).
3. Given Scale Factor:
- Here, the scale factor is \( n = \frac{1}{3} \).
- Clearly, \( 0 < \frac{1}{3} < 1 \).
4. Conclusion:
- Since \( 0 < n < 1 \), the dilation results in a reduction.
Therefore, the correct statement is:
It is a reduction because [tex]\( 0 < n < 1 \)[/tex].
Step-by-Step Solution:
1. Understanding Scale Factor:
- In geometry, a dilation is a transformation that produces an image that is the same shape as the original figure, but is a different size.
- The scale factor (\( n \)) determines whether the dilation is an enlargement or a reduction.
2. Comparison of Scale Factor:
- If \( n > 1 \), the dilation is an enlargement (the figure becomes larger).
- If \( 0 < n < 1 \), the dilation is a reduction (the figure becomes smaller).
3. Given Scale Factor:
- Here, the scale factor is \( n = \frac{1}{3} \).
- Clearly, \( 0 < \frac{1}{3} < 1 \).
4. Conclusion:
- Since \( 0 < n < 1 \), the dilation results in a reduction.
Therefore, the correct statement is:
It is a reduction because [tex]\( 0 < n < 1 \)[/tex].
