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)
“Writing fiction has developed in me an abiding respect for the unknown in a human lifetime and a sense of where to look for the threads, how to follow, how to connect, find in the thick of the tangle what clear line persists. The strands are all there: to the memory nothing is ever really lost.”
—Eudora Welty (b. 1909)
“Even though I had let them choose their own socks since babyhood, I was only beginning to learn to trust their adult judgment.. . . I had a sensation very much like the moment in an airplane when you realize that even if you stop holding the plane up by gripping the arms of your seat until your knuckles show white, the plane will stay up by itself. . . . To detach myself from my children . . . I had to achieve a condition which might be called loving objectivity.”
—Anonymous Parent of Adult Children. Ourselves and Our Children, by Boston Women’s Health Book Collective, ch. 5 (1978)