Midpoint - Cinderella Documentation
Description: The user's guide to the Interactive Geometry Software Cinderella

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# Midpoint

In this mode, the midpoint of two points can be constructed with a press–drag–release sequence. As in add a line mode, the two points can also be added.

- Pressing the left mouse button generates the first point. As in the other interactive modes, the definition of this point depends on the position of the mouse at the moment the button is pressed.
- Dragging the mouse generates the second point together with the midpoint. The second point also snaps to existing points or intersections if they are selected at the current mouse position.
- Releasing the mouse button freezes the definition. The construction is then finished.

#### Synopsis

Midpoint mode creates two points and their midpoint using a press–drag–release sequence.

#### Caution

This innocent-looking mode becomes interesting in non-Euclidean geometries. While in Euclidean geometry there is always a unique finite midpoint, in hyperbolic or elliptic geometry there are always two. Both points will be generated in this mode. In the Poincaré disk model of hyperbolic geometry, the second midpoint of two points in the disk always lies outside the disk. The presence of this point does not much matter, but there are circumstances in which one should be aware of this fact.

#### See Also

- Add a Line