Transformations What’s it all about?

Transformations A transformation is an operation that moves or changes a geometric figure in some way to produce a new figure. The new figure is called the image. Another name for the original figure is pre-image. A transformation can be shown using an arrow. ∆ABC  ∆PQR

Three main types of transformations: Translation moves every point of a figure the same distance in the same direction. Reflection uses a line of reflection to create a mirror image of the original figure. Rotation turns a figure about a fixed point, called the center of rotation . Rays drawn from the center of rotation to a point and its image form the angle of rotation.

Translations Translation moves every point of a figure the same distance in the same direction.

Reflections Reflection uses a line of reflection to create a mirror image of the original figure. Reflection video

Rotations Rotation turns a figure about a fixed point, called the center of rotation . Rays drawn from the center of rotation to a point and its image form the angle of rotation. Rotations of points and shapes Practice – student computers or iPads

Review Practice Show me/Explain Everything http://www.mathplayground.com/ShapeMods/ShapeMods.html Show me/Explain Everything Show the difference b/w: Translations Reflections Rotations Give examples of each one

Translations, reflections and rotations are three types of congruence transformations. A congruence transformation changes the position of the figure without changing its shape and size. Another name for congruence transformation is isometry. An isometry is a transformation that preserves length and angle measure.

Dilation A dilation is a transformation that stretches or shrinks a figure to create a similar figure. Dilatations produce similar figures (not congruent) In a dilation, a figure is enlarged or reduced with respect to a fixed point called the center of dilation. Dilatations are enlarged or reduced by a scale factor = the ratio of a side length of the image to the corresponding side length of the original figure. For example the new figure may be 2x bigger (enlargement) Or it may be ½ as big (reduction)