Transformations
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Transformations. transformation. A change of position or size of a figure. 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!.

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Transformations

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Transformations

Transformations


Transformation

transformation

  • A change of position or size of a figure.

  • Translations

  • Reflections

  • Rotations

  • Dilation

4 types:


Translation

translation

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

* The figures are congruent!

* The original image is slid!


Example

Example:


Reflections

reflections

  • The mirror image of the original figure

* The figures are congruent!

* The original image is flipped!


Example1

Line of Reflection

Example:


The line of reflection is also called the line of symmetry

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

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


Point of symmetry

Point of Symmetry

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


Example2

A

T

M

H

Example

Does Rhombus MATH have point symmetry?

Yes


Rotation

Fixed point

rotation

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

Example:


Another example

Another Example:


Dilation

Dilation

  • Change in size of a figure

    • Enlarge or shrink

    • Similar figures (congruent angles, proportional side lengths)


Transformations

Original Figure


Isometry

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

State whether each of the following have isometry.

  • Translation

  • Reflection

  • Rotation

  • Dilation

Yes

Yes

Yes

No


Transformationsare used to make tessellations

Transformationsare used to make tessellations


Tessellation

tessellation

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


Transformations in the work of m c escher

Transformationsin the work ofM.C. Escher


Learn more about m c escher

Learn more about M.C. Escher

  • http://www.mcescher.com/


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