HP Prime Graphing NW280AAABA manual 164

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 Eto see its polar line.

4.Tap a line and press Eto 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.

164 Geometry