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:
“It is conceivable at least that a late generation, such as we presumably are, has particular need of the sketch, in order not to be strangled to death by inherited conceptions which preclude new births.... The sketch has direction, but no ending; the sketch as reflection of a view of life that is no longer conclusive, or is not yet conclusive.”
—Max Frisch (1911–1991)
“The real dividing line between early childhood and middle childhood is not between the fifth year and the sixth year—it is more nearly when children are about seven or eight, moving on toward nine. Building the barrier at six has no psychological basis. It has come about only from the historic-economic-political fact that the age of six is when we provide schools for all.”
—James L. Hymes, Jr. (20th century)
“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)