how would you show circle C with a center of (-2,-1) and a radius of 5 is similar to circle D with a center of (4,-3) and a radius of 10??

Similar objects are objects which are the same shape but not the same size. This means they have the same angle measures and a scale factor between the side lengths. To show similarity, we can use transformations and proportions. We can translate to shift the object, dilation to increase or decrease size and so forth. We use proportions to find scsale factor or missing length.

We have a circle. Circles do not have a specific angles and all circles have 360 degrees. They do not have sides but do have radius. All circles are similar because all are the same shape - a fixed center with points equidistant from the center (the radius). To show similar we can translate the circle so the centers are the same and create a ratio between the radius.

We can translate Circle C (x+6, y-2) to have the same center as D. The ratio of radius to radius is 10/5=2. Scale factor 2 from C to D.