Distance between Images of Points under Central Dilatation Mapping

Theorem

Let $f$ be a central dilatation mapping.

Let the scale factor of $f$ be $k$.

Let $P$ and $Q$ be points in the domain of $f$.

Let $d$ be the distance between $P$ and $Q$.

Then the distance between the image of $P$ and $Q$ is $\size k d$.

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): enlargement (central dilatation, homothety, similitude)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): enlargement (central dilatation, homothety, similitude)