Reflection in the x-axis:
(x,y)=>(x,-y)
Reflection in the y-axis:
(x,y)=>(-x,y)
Reflection in the xy-diagonal:
(x,y)=>(y,x)
Written Definition:
A reflection fixes one line in the plane, called the axis of reflection,
and
exchanges
points on one side of the axis with points on the other side of the axis
at
the
same distance from the axis. In the example you see a diagonal axis in
white.
The
double ended red arrows are supposed to suggest the reflection. It's called
a
"reflection"
because similar things happen with a reflection in a mirror.
A glide reflection combines a reflection with a translation along the direction of the mirror line. Glide reflections are the only type of symmetry that involve more than one step.