Answered

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 whether the dilation of the triangle is an enlargement or a reduction based on the given scale factor \( n = \frac{1}{3} \), let's carefully analyze the problem step by step.

1. Understanding the Scale Factor:
- The scale factor \( n \) dictates by how much the figure is resized.
- If \( n > 1 \), the dilation results in an enlargement, meaning the figure increases in size.
- If \( 0 < n < 1 \), the dilation results in a reduction, meaning the figure decreases in size.
- If \( n \leq 0 \), it generally does not conform to standard geometric dilation principles, implying an invalid condition for this problem.

2. Given Scale Factor:
- You are given \( n = \frac{1}{3} \).

3. Evaluate the Given Scale Factor:
- Since \( \frac{1}{3} \) is a positive number and \( 0 < \frac{1}{3} < 1 \), this scale factor satisfies the condition for a reduction.
- Therefore, the dilation reduces the size of the original figure to \(\frac{1}{3}\) of its original dimensions.

4. Conclusion:
- Given that \( 0 < n < 1 \) with \( n = \frac{1}{3} \), it confirms that the figure undergoes a reduction.

Based on this logical analysis, the true statement regarding the dilation is:

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

Other Questions