Section 1.6 – Motion in Geometry

Transformation – basic mathematical motion

Rigid Transformations – transformations that do not change the shape or size of a figure

In geometry, the terms preimage (original) and image (new) refer to the shape that undergoes a transformation. Points on the image of an object are usually named by adding a prime symbol (‘) to the original point.

Translation – every point of a figure moves (slides) in a straight line and all points move the same distance and the same direction. The paths are parallel.

Rotation – every point of a figure moves around a given point known as the center of rotation. All points move the same angle measure.

Reflection – a line plays the role of a mirror and every point in a geometric figure is “flipped” across the line.

If a point is reflected across a line, then the line is the perpendicular bisector of the segment that connects the point with its image.

Glide Reflection – a combination of a translation and a reflection