Construct the translation-then-dilation mapping from center \((4,-3)\), radius \(5\), to center \((-2,1)\), radius \(15\). Compute the signed center displacement, form the radius ratio, and verify the enlargement while the target center stays fixed.

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Translate by ⟨−6,4⟩, then dilate by 15.

Translate by ⟨6,−4⟩, then dilate by 3.

Translate by ⟨−6,4⟩, then dilate by 1/3.

Translate by ⟨−6,4⟩, then dilate about (−2,1) by factor 3.

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Curriculum context

Course: Math II
Standard: G-C.1
Category: Geometry
Domain: Circles
Objective: Prove that all circles are similar.
Problem type: Map one circle by a specified translation-dilation composition