BuilderGrade 8⏱ 20 min
Moving shapes: transformations
Slide, flip, turn and resize a triangle on a grid, and find the coordinate rule behind each move.
Standards: 8.G.A.18.G.A.3
1Wonder
In a video game, characters slide across the screen, turn around, flip to face the other way and grow when they get a power-up. The computer does all of this with a few simple rules for moving points.
2Explore
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Turn your phone sideways, or open this lesson on a tablet or computer. The explanation and quiz below work here.
Transformation
Try this
- Slide the triangle 4 right and 3 down. What happens to every x? To every y?
- Flip it over the y-axis. Which coordinate changes sign?
- Turn it 90°, then 180°. Can you guess where A′ will land before pressing Show me?
- Resize with k = 2. Is the new triangle the same shape? The same size?
3Explain
Step 1 of 5
Translation: slide
A translation moves every point the same distance in the same direction. Sliding 4 right and 3 down adds 4 to each x and subtracts 3 from each y.
Transformations
| rule | size | |
|---|---|---|
| translation | (x, y) → (x + a, y + b) | same |
| reflection over y-axis | (x, y) → (−x, y) | same |
| rotation 90° about O | (x, y) → (−y, x) | same |
| dilation from O | (x, y) → (kx, ky) | × k |
4Practice
Question 1 of 5
The point (2, 5) is moved by the rule (x, y) → (x + 3, y − 1). Where does it land?
5Recap
- Translation slides, reflection flips, rotation turns: the image is congruent.
- Dilation resizes by a scale factor k: the image is similar.
- Each transformation is a rule for coordinates, like (x, y) → (−y, x).