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:
“In the last analysis, love is only the reflection of a man’s own worthiness from other men.”
—Ralph Waldo Emerson (1803–1882)
“I fear I agree with your friend in not liking all sermons. Some of them, one has to confess, are rubbish: but then I release my attention from the preacher, and go ahead in any line of thought he may have started: and his after-eloquence acts as a kind of accompaniment—like music while one is reading poetry, which often, to me, adds to the effect.”
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)
“In time the scouring of wind and rain will wear down the ranges and plane off the region until it has the drab monotony of the older deserts. In the meantime—a two-million-year meantime—travelers may enjoy the cruel beauties of a desert in its youth,....”
—For the State of California, U.S. public relief program (1935-1943)