Mini-Project on Translations, Reflections, and Rotations ... - Free Printable

Let's solve each part of this learning target task step by step. The goal is to identify and describe rigid transformations using precise mathematical vocabulary.

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🔹 Learning Target #1a: I can describe rigid transformations.

Rigid transformations are movements of a figure in the plane that preserve its size and shape. The three main types are:
- Translation (sliding)
- Rotation (turning around a point)
- Reflection (flipping over a line)

Now, let’s go through each section.

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## ✔ Level 2: Identify each transformation

We are given three pairs of figures (A and B). For each, determine the type of rigid transformation that maps Figure A to Figure B.

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Pair 1:

- Figure A and Figure B are mirror images.
- One is flipped across a vertical line.
- Transformation: Reflection
- Over what? A vertical line (likely the y-axis or a line between them).

✔ Answer: Reflection over a vertical line

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Pair 2:

- Figure A and Figure B are the same shape and orientation.
- But B is shifted down and to the right.
- No flipping or turning — just moved.

✔ Answer: Translation (specifically, a slide down and to the right)

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Pair 3:

- Figure A and Figure B are mirror images across a horizontal line.
- The top of A becomes the bottom of B.
- They are symmetric across a horizontal line.

✔ Answer: Reflection over a horizontal line

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## ✔ Level 3: Fully describe rigid transformations

We now need to precisely describe how Figure A is transformed to Figure B on a grid.

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First Grid:

- Figure A is a zigzag shape at the top left.
- Figure B is below and to the right.
- Let's compare coordinates.

Assume:
- Point A has a vertex at (1, 4), then (2, 3), (3, 4), (4, 3), etc.
- Figure B seems to be shifted down 3 units and right 4 units.

Let’s check:
- If you move every point of A:
→ (x + 4, y - 3)

✔ Answer:
A translation 4 units to the right and 3 units down
(or: *Translation by vector* ⟨4, -3⟩)

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Second Grid:

- Figure A is a square rotated.
- Figure B is a square but turned 90° clockwise.
- It appears to be rotated around the center of the grid.

Let’s analyze:
- The figure rotates from one orientation to another.
- All points move around a central point.
- The angle is 90 degrees clockwise.

✔ Answer:
A rotation of 90 degrees clockwise about the origin
(or: *about the center of the square*, if not at origin — but since it's centered, likely origin)

> Note: If the center of rotation isn't specified, we assume the most logical point — often the center of the figure or the origin.

So:
Rotation of 90° clockwise about the origin

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## ✔ Level 4: Describe two different types of transformations in the Navajo rug design

Look at the Navajo rug pattern.

It shows:
- Symmetric designs
- Repeating patterns
- Diamond shapes arranged in a mirrored way

Let’s identify two rigid transformations:

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✔ Transformation 1: Reflection

- The rug has vertical symmetry — left side mirrors the right side.
- You can draw a vertical line of reflection down the center.
- The design on the left is the mirror image of the right.

👉 Label: Draw a vertical dashed line down the center. Label: Line of Reflection

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✔ Transformation 2: Rotation

- Look at the diamond shapes — they repeat in a rotational pattern.
- For example, the central diamond and surrounding ones may be rotated around the center.
- Some elements appear to be rotated 180° around the center.

👉 Label: Draw a dot at the center. Label: Center of Rotation
Then show arrows indicating 180° rotation.

Alternatively, translation could also be present — repeating motifs moving up/down or left/right.

But the most evident are:
1. Reflection (left ↔ right)
2. Rotation (around center, e.g., 180°)

✔ Answer:
Two rigid transformations in the rug:
1. Reflection across a vertical line through the center.
2. Rotation of 180° about the center of the rug.

> You can draw these on the rug:
> - Vertical dashed line for reflection.
> - Arrow showing 180° turn for rotation.

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## 📌 Final Answers Summary:

Level 2: Identify Transformations

1. Reflection over a vertical line
2. Translation (right and down)
3. Reflection over a horizontal line

Level 3: Describe Transformations

1. Translation 4 units right and 3 units down
2. Rotation of 90° clockwise about the origin

Level 4: Navajo Rug

1. Reflection across a vertical line
2. Rotation of 180° about the center

> 💡 Tip: Use precise language like "reflection over the line x = 5", "rotation of 90° clockwise about the origin", etc., when possible.

Let me know if you'd like a labeled version of the rug!