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G-C.1 Warmup M2-029-A11-V03

Prove that all circles are similar.

Verify a coordinate similarity between circles

Problem

Verify the translation-then-dilation mapping between the \(\text{two}~\text{circle}~\text{equations}\). Read centers and radii, compute translation and contraction factor, map source boundary point \((2,4)\), and confirm the final point lies \(2~\text{units}\) from the target center.

Source circle A: center (−2,4), radius 4. Target circle B: center (1,8), radius 2. Open full size
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Four variants of this problem type
Curriculum context
Course
Math II
Standard
G-C.1
Category
Geometry
Domain
Circles
Objective
Prove that all circles are similar.
Problem type
Verify a coordinate similarity between circles