Verify the specified translation-then-dilation similarity. Read \(\text{both}~\text{centers}\) and radii from the equations, compute the translation vector and scale factor, map source boundary point \((4,2)\) through \(\text{both}~\text{steps}\), and confirm its final distance from the target center.
A coordinate similarity must map the center correctly and scale every radial displacement from that center by one constant. We’ll compute the center translation and radius ratio, track a boundary point through both transformations, and verify its final distance from the target center.
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