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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—Sophocles (497–406/5 B.C.)
“There’s a line between love and fascination that’s hard to see on an evening such as this.”
—Ned Washington (1901–1976)
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—Anna Howard Shaw (1847–1919)