Answer: The correct option is (A) [tex]\left(1,-\dfrac{2}{3}\right).[/tex]
Step-by-step explanation: We are given to find the co-ordinates of the image of the point R for a dilation with center (0, 0) and a scale factor of [tex]\dfrac{1}{3}.[/tex]
We can see from the given figure that
the co-ordinates of the point R are (3, -2).
Since the figure PQR is dilated with center of dilation as origin (0, 0), so the co-ordinates of the image of point R will be one-third of the co-ordinates of the point R.
Therefore, the co-ordinates of the image of R are
[tex]\dfrac{1}{3}\times (3, -2)\\\\=\left(\dfrac{3}{3},-\dfrac{2}{3}\right)\\\\\\=\left(1,-\dfrac{2}{3}\right).[/tex]
Thus, the co-ordinates of the image of point R are [tex]\left(1,-\dfrac{2}{3}\right).[/tex].
Option (A) is CORRECT.
