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–?)
“When all this is over, you know what I’m going to do? I’m gonna get married, gonna have about six kids. I’ll line ‘em up against the wall and tell them what it was like here in Burma. If they don’t cry, I’ll beat the hell out of ‘em.”
—Samuel Fuller, U.S. screenwriter, and Milton Sperling. Samuel Fuller. Barney, Merrill’s Marauders (1962)
“We’ve got to figure these things a little bit different than most people. Y’know, there’s something about going out in a plane that beats any other way.... A guy that washes out at the controls of his own ship, well, he goes down doing the thing that he loved the best. It seems to me that that’s a very special way to die.”
—Dalton Trumbo (1905–1976)