**Reflection Across A Line in The Plane**

Reflection across a line through the origin in two dimensions can be described by the following formula

Where *v* denotes the vector being reflected, *l* denotes any vector in the line being reflected in, and *v*·*l* denotes the dot product of *v* with *l*. Note the formula above can also be described as

Where the reflection of line *l* on *a* is equal to 2 times the projection of *v* on line *l* minus *v*. Reflections in a line have the eigenvalues of 1, and −1.

Read more about this topic: Reflection (mathematics)

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—David Hume (1711–1776)

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—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)