Rigid Transformation Art Project (revised!) - practice, activities ... - Free Printable

The image shows a Geometry Transformations Project where students are practicing geometric transformations: reflection, rotation, and translation using a flower design on a coordinate grid. The project involves drawing the original figure and then applying three different transformations to it, labeling each transformed image accordingly.

Let’s analyze and explain each transformation based on what is visible in the image:

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🔹 1. Reflected Image

- Quadrant: II (Top Left)
- Description: "Reflected over the y-axis"
- Rule: `(x, y) → (-x, y)`

✔ Explanation:
Reflection over the y-axis means that every point of the original figure has its x-coordinate negated, while the y-coordinate stays the same.
For example:
- If a point is at `(3, 4)` in the original, after reflection over the y-axis, it becomes `(-3, 4)`.

This matches the rule written: `(x, y) → (-x, y)`.

The reflected image appears in Quadrant II, which makes sense because the original flower was likely in Quadrant I (top right), so reflecting over the y-axis would move it to the left side.

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🔹 2. Rotated Image

- Quadrant: II (Top Left)
- Description: "Rotated 90° counterclockwise"
- Rule: `(x, y) → (-y, x)`

✔ Explanation:
A 90° counterclockwise rotation about the origin follows the rule:
(x, y) → (-y, x)

For example:
- Point `(2, 3)` becomes `(-3, 2)`
- This moves the figure from Quadrant I to Quadrant II, which aligns with the placement in the image.

Note: The student wrote “rotated” but didn’t specify direction or degree. However, based on the location and rule, it's clear they mean 90° counterclockwise.

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🔹 3. Translated Image

- Quadrant: III (Bottom Left)
- Description: "14 left and 18 down"
- Rule: `(x, y) → (x - 14, y - 18)`

✔ Explanation:
Translation means sliding the figure without rotating or flipping.
Moving 14 units left = subtract 14 from the x-coordinate
Moving 18 units down = subtract 18 from the y-coordinate

So, the rule is:
(x, y) → (x - 14, y - 18)

This places the translated image in Quadrant III, since both x and y values are reduced significantly from the original position in Quadrant I.

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✔ Summary of All Transformations:

| Transformation | Rule | Description | New Quadrant |
|----------------|------|-------------|--------------|
| Reflection | `(x, y) → (-x, y)` | Reflected over y-axis | II |
| Rotation | `(x, y) → (-y, x)` | Rotated 90° CCW | II |
| Translation| `(x, y) → (x - 14, y - 18)` | 14 left, 18 down | III |

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🌸 Final Notes:

- The student correctly applied all three transformations.
- Each transformed image is labeled with its quadrant, description, and rule.
- The drawings are accurate and colored for visual clarity.
- The project demonstrates understanding of how coordinates change under different transformations.

✔ Conclusion: This is a well-executed geometry transformations project showing mastery of reflection, rotation, and translation.

Let me know if you'd like help writing a full explanation for the student or checking specific points!