Transformations transformation A change of position or size

Transformations

transformation • A change of position or size of a figure. 1. Translations 4 types: 2. Reflections 3. Rotations 4. Dilation

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 A M T H

rotation • A transformation that turns a figure about a fixed point. 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 Yes • Reflection Yes • Rotation Yes • Dilation 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/