🧱 See It
Translate (slide), reflect (flip), and rotate (turn) — the same three moves from before. The difference now is precision: instead of just "slide it over," a coordinate rule says exactly how far and which direction, so anyone reading the rule ends up in the exact same spot.
✏️ Draw It
Point A at (−3, 1), translated 4 right and 2 down, lands on A′ at (1, −1):
The arrow shows the slide: 4 right, 2 down. Every point on a shape moves by that exact same amount.
🔢 Write It
| Move | Coordinate rule |
|---|---|
| Translate (a right, b up) | (x, y) → (x + a, y + b) |
| Reflect across the x-axis | (x, y) → (x, −y) |
| Reflect across the y-axis | (x, y) → (−x, y) |
| Rotate 180° about the origin | (x, y) → (−x, −y) |
Reflecting across the x-axis flips the value that ISN'T x — it's the y-coordinate that changes sign, not x.
💡 Worked Examples
Example 1 — Translate: (2, 3) by 4 right and 2 down
- Rule:
(x, y) → (x + 4, y − 2) - Apply:
(2 + 4, 3 − 2) - Answer:
(6, 1)
Example 2 — Reflect across the y-axis: (2, 3)
- Rule:
(x, y) → (−x, y) - Apply:
(−2, 3) - Answer:
(−2, 3)
🧠 Quick Reference
Translate changes BOTH coordinates by adding. Reflect flips the SIGN of just one coordinate (the one NOT named in "across the ___-axis"). Rotate 180° flips the sign of BOTH.