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Interpreting the Scale Factor

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
To determine the nature of the dilation, we need to interpret the scale factor \( n \) which is given as \( \frac{1}{3} \).

Step-by-Step Solution:

1. Understanding Dilation:
- Dilation is a transformation that alters the size of a figure, but not its shape.
- The scale factor \( n \) determines how much the figure will be enlarged or reduced.

2. Analyzing the Scale Factor \( n = \frac{1}{3} \):
- A scale factor \( n \) where \( 0 < n < 1 \) indicates a reduction. This means the figure is scaled down.
- A scale factor \( n \) where \( n > 1 \) indicates an enlargement. This means the figure is scaled up.

3. Applying the Given Scale Factor:
- Since \( \frac{1}{3} \) is a fraction that is greater than 0 but less than 1 (\( 0 < \frac{1}{3} < 1 \)), it falls within the reduction range.

4. Conclusion:
- Therefore, \( n = \frac{1}{3} \) produces a reduction in the size of the triangle.
- The correct statement is: \(\text{It is a reduction because } 0 < n < 1\).

So, the true statement regarding the dilation is:

It is a reduction because [tex]\(0 < n < 1\)[/tex].

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