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:
“With respect to a true culture and manhood, we are essentially provincial still, not metropolitan,—mere Jonathans. We are provincial, because we do not find at home our standards; because we do not worship truth, but the reflection of truth; because we are warped and narrowed by an exclusive devotion to trade and commerce and manufacturers and agriculture and the like, which are but means, and not the end.”
—Henry David Thoreau (1817–1862)
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Yet if it does not seem a moment’s thought,
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“As for the dispute about solitude and society, any comparison is impertinent. It is an idling down on the plane at the base of a mountain, instead of climbing steadily to its top.”
—Henry David Thoreau (1817–1862)