Transformations

transformation A change of position or size of a figure. 4 types: Translations Reflections Rotations Dilation 4 types:

translation A transformation that moves points the same distance and in the same direction. * The figures are congruent! * The original image is slid!

Example:

reflections The mirror image of the original figure * The figures are congruent! * The original image is flipped!

Example: Line of Reflection

The line of Reflection is also called the line of symmetry.

It is also possible to have a reflection image with respect to a point.

Point of Symmetry The point must be the midpoint for all segments that pass through it and have endpoints on the figure.

Example Does Rhombus MATH have point symmetry? Yes M A T H

rotation A transformation that turns a figure about a fixed point. Example:

Another Example:

Dilation Change in size of a figure Enlarge or shrink Similar figures (congruent angles, proportional side lengths)

Original Figure

isometry Congruence Transformation Maps every segment to a congruent segment No change in size! Congruent sides and congruent angles

State whether each of the following have isometry. Translation Reflection Rotation Dilation Yes Yes Yes No

Transformationsare used to make tessellations

tessellation A repeating pattern of figures that completely covers a plane without gaps or overlaps.

Transformations in the work of M.C. Escher

Learn more about M.C. Escher http://www.mcescher.com/