Problem

Construct the required translation-then-dilation mapping. Subtract source-center coordinates from target-center coordinates for the translation vector, compute target radius divided by source radius for the scale factor, and explain why dilating about the translated center keeps that center fixed.

Source and target circles: A center (1,2), radius 3; B center (5,7), radius 9.

Big Picture

What this problem is really about

A translation-dilation composition handles circle location and size in separate ordered stages. We’ll subtract centers to align them first, compare radii for the scale factor, and center the dilation at the translated point so the aligned center stays fixed.

Answer choices

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Translate by ⟨−4,−5⟩, then dilate by 3.

Translate by ⟨4,5⟩, then dilate by 1/3.

Translate by ⟨4,5⟩, then dilate about the origin by 3.

Translate by ⟨4,5⟩, then dilate about (5,7) by factor 3.

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Construct the required translation-then-dilation mapping. Subtract source-center coordinates from target-center coordinates for the translation vector, compute target radius divided by source radius for the scale factor, and explain why dilating about the translated center keeps that center fixed.

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