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Transformations

Learn about the different geometric transformations - reflections, translations, rotations, and dilations. Understand their properties, uses, and how they can change the position, size, and shape of figures.

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Transformations

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  1. Transformations

  2. transformation • One to One Mapping Preimage Point  Image Point A  A´ • A change of position or size of a figure.

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

  4. Line of Reflection Example:

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

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

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

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

  9. translation • A transformation that moves points the same distance and in the same direction. * The figures are congruent! *Often referred to as a glide!

  10. Example:

  11. Translations are a composite of Reflections • One reflection over another with respect to two parallel lines. l m

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

  13. Another Example:

  14. l m Rotations are a composite of Reflections • One reflection over another with respect to two intersecting lines. *Not drawn to scale!

  15. Center of rotation • The measure of the angle of rotation is twice the measure of the angle formed by the intersecting lines • Turn around Point

  16. dilation • Alters the size of a geometric figure, but does not change its shape.

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

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

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