Lesson 1 — Transformations
Big idea: A transformation moves or changes a figure. An isometry preserves size and shape.
Words to know
| Word | Meaning |
|---|---|
| Transformation | A rule that maps each point of a figure to an image point. |
| Translation | A slide; every point moves the same distance in the same direction. |
| Reflection | A flip over a line. |
| Rotation | A turn about a point. |
| Dilation | An enlargement or reduction about a center. |
| Isometry | A transformation that preserves distance and angle measure. |
Concepts to know
- Translation, reflection, and rotation are isometries.
- A dilation is not an isometry; it changes size.
- Isometries produce congruent figures.
- A transformation maps the original figure (preimage) to a new figure (image).
- The image is often named with primes: A′ is the image of A.
Homework helper
| If the homework asks… | Do this… |
|---|---|
| Identify the transformation | Slide → translation; flip → reflection; turn → rotation; resize → dilation. |
| Decide whether it is an isometry | Check whether size and shape stay the same. |
| Name the image point | Use the same letter with a prime: A → A′. |
| Compare preimage and image | Check corresponding sides and angles. |
| Explain why a dilation is not an isometry | Side lengths change. |
Worked example
A triangle is moved 5 units right and 3 units up.
- The transformation is a translation.
- It is an isometry, so the image triangle is congruent to the original.
- Each vertex maps to a point 5 right and 3 up.
Watch out
- A dilation changes size, so it is not an isometry.
- A reflection flips orientation; a translation and rotation do not.
- “Transformation” is the general word; “translation” is a specific type.
- Do not confuse the preimage and the image.