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G-C.1 Warmup M2-029-A11-V04

Prove that all circles are similar.

Verify a coordinate similarity between circles

Problem

Verify the mapping to \((x+1)^{2}+(y-3)^{2}=81\). Extract its center and radius, compute the source-to-target translation and scale factor, map boundary point \((7,-2)\) through \(\text{both}~\text{steps}\), and check the target radius.

Source circle A: center (4,−2), radius 3. Target circle B: equation (x+1)²+(y−3)²=81, center (−1,3), radius 9. 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