HP Prime Graphing Calculator - Manual (Page 168)

164 Geometry
lengths of the corresponding segments. If k=1, then the
lengths CA and CA’ are reciprocals.
Suppose you wish to find the inversion of a circle (GC) with a
point on the circle (GD) as center.
1. Tap
and select
More > Inversion.
2. Tap the point that is to be the center (GD) of the inversion
circle and press E .
3. Enter the inversion
ratio—use the default
value of 1—and press
E .
4. Tap on the circle( GC)
and press E .
You will see that the
inversion is a line.
Reciprocation A reciprocation is a special case of inversion involving circles.
A reciprocation with respect to a circle transforms each point
in the plane into its polar line. Conversely, the reciprocation
with respect to a circle maps each line in the plane into its
pole.
1. Tap
and select More > Reciprocation.
2. Tap the circle and press E .
3. Tap a point and press
E to see its polar
line.
4. Tap a line and press
E to see its pole.
In the illustration to the
right, point K is the
reciprocation of line DE
(G) and Line I (at the bottom of the display) is the
reciprocation of point H.