Reflection (mathematics) - Reflection Across A Line in The Plane

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.

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