Question

Circle P has center the point h comma k and radius r. Circle Q has center the point m comma n and radius s. The circles are shown on the graph.



Question
Move letters and expressions to the lines to show how transformations can be used to prove that circle P is similar to circle Q.

Response area with 6 blank spaces
Translate circle P horizontally by
Blank space 2 empty
units and vertically by
Blank space 3 empty
units.
The image, circle P prime, has center left-parenthesis
Blank space 4 empty
comma
Blank space 5 empty
right-parenthesis.

Next, dilate circle P prime by a factor of
Blank space 7 empty
. The image, circle P double prime, has radius
Blank space 8 empty
.

Since a similarity transformation exists, circle P is similar to circle Q.

Answer options with 13 options.

Answer 1

To show how transformations can be used to prove that circle P is similar to circle Q, you can fill in the blanks as follows:

1. Translate circle P horizontally by **(m - h)** units and vertically by **(n - k)** units.

The image, circle P prime, has center left-parenthesis **m** comma **n** right-parenthesis.

2. Next, dilate circle P prime by a factor of **(s/r)**. The image, circle P double prime, has radius **s**.

Thus, the completed response would be:

- Translate circle P horizontally by **(m - h)** units and vertically by **(n - k)** units.
- The image, circle P prime, has center left-parenthesis **m** comma **n** right-parenthesis.
- Next, dilate circle P prime by a factor of **(s/r)**. The image, circle P double prime, has radius **s**.

Since a similarity transformation exists, circle P is similar to circle Q.