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In mathematics, a homothety (or homothecy) is a transformation of space which dilates distances with respect to a fixed point. Such a transformation is also called an enlargement. A homothety with center $H$ and factor $k$ sends point $A$ to a point $A' \ni HA'=k\cdot HA$ This is denoted by $\mathcal{H}(H, k)$.

    • Note: Refer to this website, as denoted by the link provided here:

https://brilliant.org/wiki/euclidean-geometry-homothety/ - It provides a comprehensive overview of the subsets corresponding to this topic, as well as a few example problems and related proofs.

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