RS is 4 units.
Dilation exists in the enlarging or shrinking of a mathematical element (a point on a coordinate grid, polygon, line segment) utilizing a specific scale factor. Dilation exists as one of the five major transformations in geometry. Dilation does not vary the shape of the object from preimage to image.
If a figure stands dilated by a scale factor of k, then the measure of the corresponding image (I') of a line segment containing measure 'I' is given by:-
[tex]$l^{\prime}=k l$[/tex]
Given: Square RSTU dilates by a factor of $1 \backslash 2$ regarding the origin to make square R'S'T'U'.
The measure of line segment [tex]$R^{\prime} S^{\prime}=2$[/tex] units
The scale factor [tex]$: k=\frac{1}{2}$[/tex]
Utilizing the above equation, we have
[tex]&R^{\prime} S^{\prime}=\frac{1}{2} R S \\[/tex]
[tex]&\Rightarrow R S=2 \times R^{\prime} S^{\prime} \\[/tex]
[tex]&\Rightarrow R S=2 \times 2=4[/tex]
Thus, RS = 4 units.
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