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:
“Fanny was not there! How she would have enjoyed the scene.... I could not but think of her, and in spite of my efforts to prevent, the unbidden tear would flow. Alas! I cannot feel the satisfaction some appear to do in the reflection that her eyes beheld the scene from the other world.”
—Rutherford Birchard Hayes (1822–1893)
“This wild night, gathering the washing as if it were flowers
animal vines twisting over the line and
slapping my face lightly, soundless merriment
in the gesticulations of shirtsleeves ...”
—Denise Levertov (b. 1923)
“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)