Final answer:
None of the given options, A through D, represent the correct algebraic representation of the dilation that moves vertex R to R', as the correct transformation based on the given coordinates is (x, y) → (⅓x, ⅓y), which shrinks the rectangle to one-third of its original size both horizontally and vertically.
Step-by-step explanation:
The question is asking for the algebraic representation of a dilation transformation that moves vertex R of a rectangle to a new position R'. Given the original coordinates of R(-3, 3) and the new coordinates of R'(-1, 1), we can determine the scale factor of the dilation and the corresponding algebraic representation.
To find the scale factor, we consider the ratio of the new coordinates to the original coordinates. The x-coordinate moved from -3 to -1, which is a change by a factor of 1/3, and the y-coordinate moved from 3 to 1, also a change by a factor of 1/3. Since both the x and y scale factors are the same, this indicates a uniform dilation.
Based on the scale factor, we can then look for an option that matches this transformation. Option C, which suggests the transformation as (x, y) → (2x, 2y), would obviously double the size of the rectangle, not reduce it to one-third. Therefore, the correct algebraic representation for this dilation is none of the options presented: A, B, C, or D. This seems to be an error since the correct transformation would be (x, y) → (⅓x, ⅓y) to shrink the rectangle to one-third of its size in both the x and y directions.