CK12 - Geometry

Finally, we can showthat is the perpendicularbisectorof.

• Midpointof is.


• Midpointof is on ( - and -coordinatesof are the same).


• is the perpendicularbisectorof.

Conclusion: and are reflectionsin the line.

Example 2

Point is reflectedin the line. The imageis. is then reflectedin the -axis.The

imageis. Whatare the coordinatesof?

We find one reflectionat a time.

• Reflect in is.


• 
  

  Reflect in the -axis. is.

  
  

ReflectionsAre Isometries

Areflectionin a lineis anisometry.Distancebetweenpointsis “preserved”(staysthe same).

We will verifythe isometryfor reflectionin the -axis.The storyis very similarfor reflectionin the -axis.

You can writea proofthat reflectionin is an isometryin the LessonExercises.

The diagrambelowshows and its reflectionin the -axis,.