🧱 See It
Cut a shape out of paper (or use tracing paper) and try all three moves with your hands:
- Translation — slide the cutout sideways or up/down. It doesn't turn, and it doesn't flip. It just moves.
- Reflection — flip the cutout over, like looking at it in a mirror. Left and right (or top and bottom) swap.
- Rotation — pin one point down with your finger and spin the cutout around that point, like a clock hand.
Same shape, same size, every time — only its position or orientation changes.
✏️ Draw It
Here's one triangle, then three copies — each one made with a single move:
Original
Translation
Reflection
Rotation
Every copy is the exact same size and shape as the original. Only its position or orientation is different.
🔢 Write It
To describe a transformation precisely — so someone else could redo it exactly — say what kind of move it is, and give the details:
| Move | How to describe it |
|---|---|
| Translation | translate 3 units right, 2 units down |
| Reflection | reflect across the y-axis |
| Rotation | rotate 90° clockwise about the origin |
The description applies to every point of the shape at once — not just one corner.
💡 Worked Examples
Example 1 — Translate, then Reflect: Start with point (2, 3).
- Shape A is at
(2, 3). - Apply the translation "3 units right": add 3 to the x-coordinate. Shape B is at
(5, 3). - Apply the reflection "across the y-axis": flip the sign of the x-coordinate. Shape C is at
(−5, 3). - Final answer:
(−5, 3).
Example 2 — Same moves, reversed order: Start with the same point (2, 3).
- Shape A is at
(2, 3). - Apply the reflection "across the y-axis" first: flip the sign of the x-coordinate. Shape B is at
(−2, 3). - Apply the translation "3 units right": add 3 to the x-coordinate. Shape C is at
(1, 3). - Final answer:
(1, 3)— different from Example 1! Order matters.
🧠 Quick Reference
3 moves: Translate (slide), Reflect (flip), Rotate (turn). When combining moves, do them ONE AT A TIME, in order, and label each in-between result (A → B → C) — never try to do two moves in your head at once.
| Move | What changes | What stays the same |
|---|---|---|
| Translate | Position | Size, shape, orientation |
| Reflect | Orientation (mirrored) | Size, shape |
| Rotate | Orientation (turned) | Size, shape, distance from center |