Finding the Isometry with One MoveBelow are two situations for isometries. You could have an isometry that moves three points to three points that preserves the orientation of the three points. This orientation would be a rotation. The center point is the perpendicular bisectors of the segments that connect corresponding vertices. (These are shown in red.) Move the Slider to see the roation of the triangle. The one on the right is what happens when the isometry is not orientation preserving. If this happens the isometry is a glide reflection. The line of reflection is the line that connects the midpoints of the segments that join corresponding vertices. Then you must translate by a vector parallel to this line. Check by doing the reflection over the line. Then translate by the purple vector.
Jackie Southard, August 7, 2008, Created with GeoGebra |