Circle 1 is centered at (−4, 5) and has a radius of 2 centimeters. Circle 2 is centered at (2, 1) and has a radius of 6 centimet
ers. What transformations can be applied to Circle 1 to prove that the circles are similar? Enter your answers in the boxes. The circles are similar because you can translate Circle 1 using the transformation rule ( , ) and then dilate it using a scale factor of
Basically, you have two circles. You are asked to take circle 1 and "move it" so that it is on top of circle 2. This process of moving is called a translation and can be thought of as sliding. You do this by ensuring that the two have the same center. So, starting at (-4,5) how do you have to move to end up at (2,1)?
To do this we need to move right 6 as the x-coordinate goes from -4 to 2. We also need to move down 4 as the y-coordinate goes from 5 to 1. So we add 6 to the x-coordinate and subtract 4 from the y-coordinate. The transformation rule is (x+6, y-4).
Once you do this the circles have the same center. Next you wish to dilate circle 1 so it ends up being the same size at circle 2. That means you stretch it out in such a way that it keeps its shape. Circle 1 has a radius of 2 centimeters and circle 2 has a radius of 6 centimeters. That is 3x bigger. So we dilate by a factor of 3.
Translations and dilations (along with reflections and rotations) belong to a group known as transformations.
Cole can learn how to play tennis. But if he saved the money, he can save up and get something bigger, or save up for college. There is only so much he can do with a tennis racket except for using it to learn a new sport.
