We now havethesereflectionsof :
- Reflectionof in the -axisis.
[ -coordinatestaysthe same, -coordinatebecomesopposite]- Reflectionof in the -axisis.
[ -coordinatebecomesopposite, -coordinatestaysthe same]- Reflectionof in the line is.
[switchthe - and -coordinates]A look is enoughto convinceus of the first two reflections.We’ll provethe third one.
Example 1
Provethat the reflectionof point in the line is the point.Hereis an “outline”proof.First,we knowthe slopeof- Slopeof is 1.
Next,let's assumeinvestigatethe slopeof.- Slopeof is.
Therefore,we havejust shownthat and are perpendicular.- is perpendicularto (productof slopesis ).