To determine whether each scale factor represents an expansion or a contraction, let's review the definitions of these terms in the context of dilation:
- Expansion: A dilation where the absolute value of the scale factor is greater than 1. This means that the object is stretched.
- Contraction: A dilation where the absolute value of the scale factor is less than 1. This means that the object is shrunk.
Now, we'll classify each of the given scale factors based on these definitions.
1. Scale factor: [tex]\(-\frac{3}{5}\)[/tex]
- The absolute value is [tex]\(\left|-\frac{3}{5}\right| = \frac{3}{5} = 0.6\)[/tex], which is less than 1.
- Therefore, [tex]\(-\frac{3}{5}\)[/tex] is a contraction.
2. Scale factor: [tex]\(\frac{1}{10}\)[/tex]
- The absolute value is [tex]\(\left|\frac{1}{10}\right| = 0.1\)[/tex], which is less than 1.
- Therefore, [tex]\(\frac{1}{10}\)[/tex] is a contraction.
3. Scale factor: 2.33
- The absolute value is [tex]\(\left|2.33\right| = 2.33\)[/tex], which is greater than 1.
- Therefore, 2.33 is an expansion.
4. Scale factor: -6
- The absolute value is [tex]\(\left|-6\right| = 6\)[/tex], which is greater than 1.
- Therefore, -6 is an expansion.
Based on these classifications, the filled-out table should look as follows:
[tex]\[
\begin{tabular}{|c|c|c|}
\hline Scale factor & Expansion & Contraction \\
\hline -\frac{3}{5} & 0 & 1 \\
\hline \frac{1}{10} & 0 & 1 \\
\hline 2.33 & 1 & 0 \\
\hline -6 & 1 & 0 \\
\hline
\end{tabular}
\][/tex]
Each scale factor has been correctly described as either an expansion or a contraction.
