Overview

reflection


'reflection' can also refer to...

reflection

reflection

reflection

reflection

reflection

reflection

Reflections

Reflections

Reflections Pursuing Projects, Following Policies

Reflections Tailwinds, Turning Points

Reflections Headwinds, Hollowing Out

Reflections

Reflections

Reflection Eternity and World-Cycles

Reflection Eternity and Astrology in the Work of Vettius Valens

Reflection The Kaddish

Reflection Moral Motivation and the Limits of Moral Agency in Literary Naturalism Dreiser’s Sister Carrie

Reflection Cicero on Moral Motivation and Seeing (How) to Be Good

Reflection “Eternalists” and “Materialists” in Islam: A Note on the Dahriyya

Reflection Borges on Eternity

 

More Like This

Show all results sharing this subject:

  • Mathematics

GO

Show Summary Details

Quick Reference

(of the plane)

Let l be a line in the plane. Then the mirror-image of a point P is the point P′ such that PP′ is perpendicular to l and l cuts PP′ at its midpoint. The reflection of the plane in the line l is the transformation of the plane that maps each point P to its mirror-image P′. Suppose that the line l passes through the origin O and makes an angle α with the x-axis. If P has polar coordinates (r, θ), its mirror-image P′ has polar coordinates (r, 2α−θ). In terms of Cartesian coordinates, reflection in the line l maps P with coordinates (x, y) to P′ with coordinates (x′, y′), where

x′ = x cos 2α + y sin 2α,

y′ = x sin 2α − y cos 2α.

Subjects: Mathematics.


Reference entries

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.