Pre-Algebra
Geometry
Transformations (translations, reflections, rotations, dilations)
20 practice questions
0 video lessons
Theory + worked examples
Transformations
Texas Pre-Algebra (TEKS) • Standard 8.10(A) • Geometry
Transformations is a topic in Geometry in the Texas Essential Knowledge and Skills. It is aligned to Standard 8.10(A), 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.
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 slides a figure.
The four transformations.
Two kinds:
\[\text{rigid: slide, flip, turn}\quad\text{non-rigid: resize}\]
Rigid motions produce congruent images.
How to identify a transformation
- Compare the image to the original.
- Same size, moved over: translation.
- Mirror image: reflection; turned: rotation.
- Bigger or smaller: dilation.
Example 1 — Rigid or not
Which transformation changes size?
Solution
A dilation.
Example 2 — Translation
What does a translation do?
Solution
Slides every point the same distance and direction.
Example 3 — Congruence
Which transformations preserve size and shape?
Solution
Translation, reflection, and rotation.
Example 4 — Reflection
What does a reflection produce?
Solution
A mirror image across a line.
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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Volume of cylinders, cones and spheres
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