Question

Select all the transformation statements which prove that circle p and q are similar

Answer 1

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:

`(x,y)\to(x-5,y+6)_{}`

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:

`\begin{gathered} (x,y)\to(x+5,y-6) \\ D_{(8)/(5)} \end{gathered}`

So option C is also correct.