Geometry: An Interactive Journey to Mastery

Lesson 30: The Mathematics of Symmetry

The Mathematics of Symmetry

Lesson 30

Topics

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x dilation: A dilation in the plane from a point O with scale factor k is the mapping that takes each point

P different from O to a point Pc on the ray OPJJJG such that OPc kOP. The dilation keeps the point O

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x JOLGHUHÀHFWLRQ$JOLGHUHÀHFWLRQDORQJDOLQHL in a plane is the mapping that results from performing

a translation in a direction parallel to LIROORZHGE\DUHÀHFWLRQDERXWL.

x isometry: A mapping that preserves distances between points.

x mapping: A mapping of the plane is a rule that shifts some or all points of the plane to new locations

in the plane.

x UHÀHFWLRQ$UHÀHFWLRQLQDSODQHDERXWDOLQHL is a mapping that takes each point P in the plane not on

L to a point Pc so that L is the perpendicular bisector of PPc. It keeps each point on L¿[HGLQSODFH

x rotation: A rotation in the plane about a point O through a counterclockwise angle of x° is the mapping

that takes each P in the plane different from O to a point Pc such that the line segments OP and OPc

are congruent and the angle from OP to OPc, measured in a counterclockwise direction, is x°. The

rotation keeps the point OLWVHOI¿[HGLQSODFH

x symmetry$¿JXUHLVVDLGWRKDYHV\PPHWU\LIWKHUHLVDPDSSLQJRIWKHSODQHWKDWSRLQWVWKH¿JXUH

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x translation$WUDQVODWLRQLQDSODQHLVDPDSSLQJWKDWVKLIWVHDFKSRLQWRIWKHSODQHD¿[HGGLVWDQFHLQ

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