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:
“The reflection of her here, and then there,
Is another shadow, another evasion,
Another denial. If she is everywhere,
She is nowhere, to him.
But this she has made.”
—Wallace Stevens (1879–1955)
“Men are not to be told anything they might find too painful; the secret depths of human nature, the sordid physicalities, might overwhelm or damage them. For instance, men often faint at the sight of their own blood, to which they are not accustomed. For this reason you should never stand behind one in the line at the Red Cross donor clinic.”
—Margaret Atwood (b. 1939)
“with the plane nowhere and her body taking by the throat
The undying cry of the void falling living beginning to be something
That no one has ever been and lived through screaming without enough air”
—James Dickey (b. 1923)