The center of rotation is the ONLY point in the plane that is unaffected by a rotation. If point P is NOT point O, then OP = OP’Ģ.
Rays drawn from the center of rotation to a point and its image form an angle called the angle of rotationĪn object and its rotation are the same shape and size, but the figures may be turned in different directions.Ī rotation about a Point O through Θ degrees is an isometric transformation that maps every point P in the plane to a point P’, so that the following properties are true ġ. The pre-image (D) = image (D’) when the point is on the line of reflection.Ī rotation is an isometric transformation that turns a figure about a fixed point called the center of rotation.
ORIENTATION IS REVERSED – The pre-image has a reversed orientation than its image.Notice that because line m is the perpendicular to, and they are all parallel to each other. Points farther away from the line of reflection move a greater distance than those closer to the line of reflection. DISTANCES ARE DIFFERENT - Points in the plane move different distances, depending on their distance from the line of reflection.TRANSFORMATION PROPERTIES – Because a reflection is a transformation that maps all points the perpendicular distance on the opposite side of the line of reflection the following properties are present. Collinearity (points on a line, remain on the line)Īfter a reflection, the pre-image and image are identical.Parallelism (things that were parallel are still parallel).Distance (lengths of segments are the same).
ISOMETRIC PROPERTIES - Because a reflection is an isometric transformation the following properties are preserved between the pre-image and its image: The isometric properites help us build concepts to congruence, and the transformation properties help us understand the specific properties of that motion in the plane.
TEACHER NOTE - Each of these transformations have ISOMETRIC properties and TRANSFORMATION properties. If point P is NOT on line m, then line m is the perpendicular bisector of. The line of reflection is the perpendicular bisector of the segment joining every point and its image.Ī reflection in a line m is a isometric transformation that maps every point P in the plane to a point P’, so that the following properties are true ġ. Because a reflection is an isometry, the image does not change size or shape. (x,y)\rightarrow (−x,−y)\).High School Geometry Common Core G.CO.A.4 - Transformations - Teacher Notes - PattersonĬONCEPT 1 - Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular line, parallel lines, and line segment.Ī reflection over a line m (notation R m) is an isometric transformation in which each point of the original figure (pre-image) has an image that is the same distance from the line of reflection as the original point but is on the opposite side of the line.