Try this.- Drawa line.
- Drawa triangle.
- Reflectthe trianglein the line.
- Lookat your results.
- Repeatwith differentlines,and figuresotherthan a triangle.
Now try this.- Drawa line
- Drawa point.
- Reflectthe pointin the line.
- Connectthe pointand its reflectionwith a segment.
- Measurethe distanceof the originalpointto the line, and the distanceof the reflectedpointto the line.
- Measurethe angleformedby the originalline and the segmentconnectingthe originalpointand its re-
flection.
Let’s put this informationin morepreciseterms.
Reflectionof a Pointin a Line:Point is thereflectionof point in line if and only if line is the perpendicular
bisectorof.Reflectionsin SpecialLines
In a coordinateplanethereare some“special”lines for whichit is relativelyeasyto createreflections.
- the axis
- the axis
- the line (this line makesa anglebetweenthe and axes)
We can developsimpleformulasfor reflectionsin theselines.
Let be a pointin the coordinateplane.