HP Prime Graphing NW280AAABA manual Inversion, Projection, Reflection

inversion

Draws the inversion of a point, with respect to another point, by a scale factor.

inversion(point1, realk, point2)

Example:

inversion(GA, 3, GB) draws point C on line AB such that AB*AC=3. In this case, point A is the center of the inversion and the scale factor is 3. Point B is the point whose inversion is created.

In general, the inversion of point A through center C, with scale factor k, maps A onto A’, such that A’ is on line CA and CA*CA’=k, where CA and CA’ denote the lengths of the corresponding segments. If k=1, then the lengths CA and CA’ are reciprocals.

projection

Draws the orthogonal projection of a point onto a curve.

projection(curve, point)

reflection

Reflects a geometric object over a line or through a point. The latter is sometimes referred to as a half-turn.

reflection(line, object) or reflection(point, object)

Examples:

reflection(line(x=3),point(1,1)) reflects the point at (1, 1) over the vertical line x=3 to create a point at (5,1).

reflection(1+i, 3-2i)reflects the point at (3,–2) through the point at (1, 1) to create a point at (–1, 4).

Geometry 179