Editing Reflection (mathematics) (section)

==Construction==
[[File:Perpendicular-construction.svg|thumb|236px|Point {{mvar|Q}} is the reflection of point {{mvar|P}} through the line {{mvar|AB}}.]]

In a plane (or, respectively, 3-dimensional) geometry, to find the reflection of a point drop a [[perpendicular]] from the point to the line (plane) used for reflection, and extend it the same distance on the other side. To find the reflection of a figure, reflect each point in the figure.

To reflect point {{math|P}} through the line {{math|AB}} using [[compass and straightedge]], proceed as follows (see figure):

* Step 1 (red): construct a [[circle]] with center at {{math|P}} and some fixed radius {{math|''r''}} to create points {{math|A′}} and {{math|B′}} on the line {{math|AB}}, which will be [[equidistant]] from {{math|P}}.
* Step 2 (green): construct circles centered at {{math|A′}} and {{math|B′}} having radius {{math|''r''}}. {{math|P}} and {{math|Q}} will be the points of intersection of these two circles.

Point {{math|Q}} is then the reflection of point {{math|P}} through line {{math|AB}}.