In order to create a transformation from circle P to Q, first let's analyse the difference in x and y-coordinates of their centers.
From P to Q, the difference in x-coordinates is -5 units, and the difference in y-coordinates is 6 units, so we have the translation:
[tex](x,y)\to(x-5,y+6)_{}[/tex]
Then, we can see that the radius decreases from 8 to 5, so we have a dilation of 5/8.
Therefore, a correct option is A.
Now, we can also create the transformation from circle Q to P. To do so, we just need to change the signal of the x and y differences and invert the fraction in the dilation.
So we would have:
[tex]\begin{gathered} (x,y)\to(x+5,y-6) \\ D_{\frac{8}{5}} \end{gathered}[/tex]
So option C is also correct.
