Start by creating two different circles:

• create a point, and label itA. To make the remainder of the activity easier, choose integers for thexandycoordinates of pointA.
• Create a circle with its center at pointAand with a radius of your choice.To make the remainder of the activity easier, choose an integer value for the radius.
• Create a another point, and label itB. To make the remainder of the activity easier, choose integers for thexandycoordinates of the point.
• Create a circle with its center at pointBand with a radius of your choice that is different from the radius chosen for circleA. To make the remainder of the activity easier, choose an integer value for the radius.

Take a screenshot of the two circles you created, save it, and insert the image in the space provided.

Part B

Recall what you know about similarity.If circleBis similar to circleA, what must exist?

Part C

What is the difference of thex-coordinate of pointAand thex-coordinate of pointB?

Part D

In terms of rigid transformations (reflections, rotations, and translations), what does this difference represent?

Part E

What is the difference of they-coordinate of pointAand they-coordinate of pointB?

Part F

In terms of rigid transformations (reflections, rotations, and translations), what does this difference represent?

Part G

What is the ratio of the radius of circleAto the radius of circleB?

Part H

In terms of nonrigid transformations, what does this ratio represent?

Part I

Write a sequence of dilations and translations that maps circleBonto circleA.

Part J

What is the relationship between circleAand circleB?

Part K

You have established that circlesAandBare similar.What conclusion can you make about any two given circles?

Part L

For assurance that the similarity proof can be generalized to all circles, try more examples of creating two circles and determining the similarity transformations that map one circle onto the other circle.Take a screenshot of two such circles, labeledCandD, that are different from the ones created in part A, save it, and insert the image in the space provided.

Part M

Write a sequence of dilations and translations that maps circleDonto circleCand that shows the two circles you created are similar.