Image of Point under Negative Scale Factor

Theorem

Let $f$ be a central dilatation mapping with center of enlargement $C$.

Let the scale factor of $f$ be negative.

Let the image of a point $P$ be $P'$.

Then $PCP'$ is a straight line such that $C$ is between $P$ and $P'$.

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)