By definition, Dilation is a transformation in which the Image (the figure obtained after the transformation) and the Pre-Image (the original figure) have the same shape, but they have different size.
In this case, you know have the following vertex (the Pre-Image):
[tex]R(-9,9)[/tex]And you know that it is dilated, centered at the origin, with the following scale factor:
[tex]s.factor=\frac{1}{3}[/tex]Therefore, the rule for this transformation is:
[tex](x,y)\rightarrow(\frac{1}{3}x,\frac{1}{3}y)[/tex]Based on this, you get:
[tex]R(-9,9)\rightarrow R^{\prime}(\frac{-9}{3},\frac{9}{3})\rightarrow R^{\prime}(-3,3)[/tex]Therefore, the answer is:
[tex]R^{\prime}(-3,3)[/tex]