Question

Circle P has center P(2,0) and a radius 20. Circle Q has center Q(0,4) and radius 2. Describe the rule for translating center Q onto center P. Determine the scale factor for dilating circle Q so that it has the same radius as circle P. Are circles P & Q similar? Explain your answer

Answer 1

The circle the has a center P(2,0) is bigger than compared to the circle with the center Q(0,4) because the former has a radius 20, while the latter has a radius of only 2. You can view the graph here: 
https://www.desmos.com/calculator/od1pwqylou

(a) Describe the rule for translating center Q onto center P. By moving the center of circle Q overlapping the center of circle P, then we need to move it two units left and 4 units up.

(b) Determine the scale factor for dilating circle Q so that it has the same radius as circle P. In getting the scale factor, we need to compare the radius
= 2/10
= 1/10
So, the scale factor is 1/10

(c) Are circles P and Q similar? Explain your answer.
Yes, by applying a dilation value, circle Q can be transformed to circle P, vice versa.