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A triangle is dilated by a scale factor of [tex]n=\frac{1}{3}[/tex]. Which statement is true regarding the dilation?

A. It is a reduction because [tex]n\ \textgreater \ 1[/tex].
B. It is a reduction because [tex]0\ \textless \ n\ \textless \ 1[/tex].
C. It is an enlargement because [tex]n\ \textgreater \ 1[/tex].
D. It is an enlargement because [tex]0\ \textgreater \ n\ \textgreater \ 1[/tex].

Sagot :

GinnyAnsweridn
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].
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