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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].



Answer :

GinnyAnswer
Let's analyze the given problem step-by-step to determine which statement accurately describes the dilation of the triangle.

1. Understanding Dilation and Scale Factor:
- Dilation is a transformation that changes the size of a figure but not its shape.
- A scale factor, \( n \), determines how much the figure is enlarged or reduced.
- If \( n \) is greater than 1 (\( n > 1 \)), the figure is enlarged.
- If \( n \) is between 0 and 1 (\( 0 < n < 1 \)), the figure is reduced.

2. Given Scale Factor:
- The given scale factor is \( n = \frac{1}{3} \).

3. Analyzing the Scale Factor:
- The value of \( n \) is \( \frac{1}{3} \).
- Since \( \frac{1}{3} \) is between 0 and 1 (i.e., \( 0 < \frac{1}{3} < 1 \)), the triangle will be reduced in size.

4. Determining the Correct Statement:
- Considering \( 0 < \frac{1}{3} < 1 \), we can conclude that the dilation results in a reduction of the size of the triangle.

Therefore, the correct statement is:
- "It is a reduction because \( 0 < n < 1 \)."

So, the true statement regarding the dilation is that:
- It is a reduction because [tex]\( 0 < n < 1 \)[/tex].

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