CK12 - Geometry

Reflections

LearningObjectives

• Find the reflectionof a pointin a line on a coordinateplane.


• Multiplymatrices.


• Applymatrixmultiplicationto reflections.


• Verify that a reflectionis an isometry.

Introduction

You studiedtranslationsearlier, and saw that matrixadditioncan be usedto representa translationin a
coordinateplane.You also learnedthat a translationis an isometry.

In this lesson,we will analyzereflectionsin the sameway. This time we will use a new operation,matrix
multiplication,to representa reflectionin a coordinateplane.We will see that reflections,like translations,
are isometries.

You will havean opportunityto discoverone surprising—orevenshocking!—factof matrixarithmetic.

Reflectionin a Line

Areflectionin a line is as if the line werea mirror.

An objectreflectsin the mirror, and we see the imageof the object.

• The imageis the samedistancebehindthe mirroras the objectis in front of the mirror.


• The “line of sight”from the objectto the mirroris perpendicularto the mirroritself.


• The “line of sight”from the imageto the mirroris also perpendicularto the mirror.

TechnologyNote- GeometrySoftware

Use your geometrysoftwareto experimentwith reflections.