To find the original side length \( RS \) of square \( RSTU \) before dilation, start by understanding the effect of the dilation transformation.
Given:
- The dilation factor is \(\frac{1}{2}\).
- The side length \( R'S' \) of the dilated square \( R'S'T'U' \) is 2 units.
The dilation factor tells us how much each side length of the original square is scaled to obtain the side length of the dilated square. Specifically, a dilation factor of \(\frac{1}{2}\) means that the side length of the original square is reduced to half its original length.
To reverse this calculation and find the original side length \( RS \), we need to divide the side length of the dilated square by the dilation factor. Mathematically, we can express this relationship as:
[tex]\[
\text{Side length of original square} = \frac{\text{Side length of dilated square}}{\text{Dilation factor}}
\][/tex]
Plugging in the given values:
[tex]\[
RS = \frac{R'S'}{\frac{1}{2}} = \frac{2}{\frac{1}{2}} = 2 \times 2 = 4 \, \text{units}
\][/tex]
Therefore, the original side length \( RS \) of the square \( RSTU \) is \( 4 \) units.
The correct answer is:
C. 4 units
