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Pre-Algebra Geometry

Transformations (translations, reflections, rotations, dilations)

20 practice questions 0 video lessons Theory + worked examples

Transformations

California Pre-Algebra • Standard 8.G.3 • Geometry

Transformations is a topic in Geometry in the California Common Core State Standards. It is aligned to Standard 8.G.3, which requires students to describe the effect of translations, reflections, rotations, and dilations.

Transformations move figures: translations slide, reflections flip, rotations turn, and dilations resize.

California Pre-Algebra › Geometry › Transformations  —  Standard 8.G.3

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Theory

A transformation moves a figure:

  • Translation: a slide.
  • Reflection: a flip across a line.
  • Rotation: a turn about a point.
  • Dilation: a resize by a scale factor.
Translations, reflections, and rotations keep size and shape; dilations change size.
A translation Transformations move a figure by translation, reflection, rotation, or dilation. slide translation (a rigid motion)
A translation slides a figure.
Transformations Transformations Transformations translation: slide reflection: flip rotation: turn dilation: resize
The four transformations.

Two kinds:

\[\text{rigid: slide, flip, turn}\quad\text{non-rigid: resize}\]
rigid motions preserve size; dilations change it
Rigid motions produce congruent images.

How to identify a transformation

  1. Compare the image to the original.
  2. Same size, moved over: translation.
  3. Mirror image: reflection; turned: rotation.
  4. Bigger or smaller: dilation.
Example 1 — Rigid or not
Which transformation changes size?
Solution

A dilation.

a dilation
Example 2 — Translation
What does a translation do?
Solution

Slides every point the same distance and direction.

slides the figure
Example 3 — Congruence
Which transformations preserve size and shape?
Solution

Translation, reflection, and rotation.

translation, reflection, and rotation
Example 4 — Reflection
What does a reflection produce?
Solution

A mirror image across a line.

a mirror image

Common pitfalls

Only dilations change size.
Rigid motions keep the figure congruent.
A reflection reverses orientation.

Frequently asked questions

What is a translation?

A slide of the whole figure.

What is a dilation?

A resize by a scale factor.

Which transformations preserve size?

Translation, reflection, rotation.

What does a reflection do?

Flips the figure across a line.

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