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:
“Women generally should be taught that the rough life men must needs lead, in order to be healthy, useful and manly men, would preclude the possibility of a great degree of physical perfection, especially in color. It is not a bad reflection to know that in all probability the human animal has endowments enough without aspiring to be the beauty of all creation as well as the ruler.”
—Caroline Nichols Churchill (1833–?)
“The English never draw a line without blurring it.”
—Winston Churchill (1874–1965)
“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)