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)
Famous quotes containing the words reflection, line and/or plane:
“A little reflection will enable any person to detect in himself that setness in trifles which is the result of the unwatched instinct of self-will and to establish over himself a jealous guardianship.”
—Harriet Beecher Stowe (1811–1896)
“In order to get to East Russet you take the Vermont Central as far as Twitchell’s Falls and change there for Torpid River Junction, where a spur line takes you right into Gormley. At Gormley you are met by a buckboard which takes you back to Torpid River Junction again.”
—Robert Benchley (1889–1945)
“It was the most ungrateful and unjust act ever perpetrated by a republic upon a class of citizens who had worked and sacrificed and suffered as did the women of this nation in the struggle of the Civil War only to be rewarded at its close by such unspeakable degradation as to be reduced to the plane of subjects to enfranchised slaves.”
—Anna Howard Shaw (1847–1919)