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Transformations

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Transformations

- A change of position or size of a figure.

- Translations
- Reflections
- Rotations
- Dilation

4 types:

- A transformation that moves points the same distance and in the same direction.

* The figures are congruent!

* The original image is slid!

- The mirror image of the original figure

* The figures are congruent!

* The original image is flipped!

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.

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

A

T

M

H

Does Rhombus MATH have point symmetry?

Yes

Fixed point

- A transformation that turns a figure about a fixed point.

Example:

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

Original Figure

- Congruence Transformation
- Maps every segment to a congruent segment

- No change in size!
- Congruent sides and congruent angles

- Translation
- Reflection
- Rotation
- Dilation

Yes

Yes

Yes

No

Transformationsare used to make tessellations

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

Transformationsin the work ofM.C. Escher

- http://www.mcescher.com/