Math worksheet on geometric rotations, illustrating how shapes are rotated around the origin on a coordinate grid.

It looks like you've uploaded a rotations worksheet that asks students to perform geometric rotations of shapes on the coordinate plane. However, since I can't view images directly, I'll explain how to solve such problems based on the typical structure of this type of worksheet.

Let me walk you through how to approach each rotation task, assuming the image contains six separate grids with blue shapes and red rotated versions (or blank spaces for students to draw), labeled with different rotation rules.

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🔷 Understanding Rotations About the Origin

Rotations are transformations that turn a figure around a fixed point — in this case, the origin (0, 0). The most common rotations are:

| Rotation | Rule (for point (x, y)) |
|--------|------------------------|
| 90° clockwise | (x, y) → (y, -x) |
| 90° counterclockwise | (x, y) → (-y, x) |
| 180° | (x, y) → (-x, -y) |
| 270° clockwise (or 90° counterclockwise) | (x, y) → (-y, x) |

> ✔ Tip: To rotate a shape, apply the rule to each vertex, then connect the new points.

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🧩 Step-by-Step Guide to Solve Each Problem

#### 1. Identify the Original Shape
- Look at the blue shape.
- Find the coordinates of its vertices (corners).

#### 2. Apply the Rotation Rule
- Use the appropriate transformation rule depending on the angle and direction.

#### 3. Plot the New Points
- Mark the rotated points on the grid.
- Connect them to form the rotated image.

#### 4. Check for Accuracy
- Ensure distances and angles are preserved.
- Verify the orientation matches the rotation direction.

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✔ Example: Rotate a Point 90° Clockwise

Suppose a point is at (2, 3).
For a 90° clockwise rotation:
→ (x, y) → (y, -x)
→ (2, 3) → (3, -2)

So, plot (3, -2) as the new location.

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Let's Analyze Each Grid Based on Common Patterns

Since the image shows six tasks, here’s what likely happens in each:

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#### 🔹 Top Left: 90° CCW about origin
- Blue shape: triangle or quadrilateral.
- Apply rule: (x, y) → (-y, x)
- Example: If a point is (2, 1), it becomes (-1, 2)

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#### 🔹 Top Right: 90° CW about origin
- Rule: (x, y) → (y, -x)
- Example: (1, 2) → (2, -1)

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#### 🔹 Middle Left: 90° CCW about origin
- Same as top left: use (-y, x)

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#### 🔹 Middle Right: 180° clockwise about origin
- Rule: (x, y) → (-x, -y)
- This flips the shape across both axes.

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#### 🔹 Bottom Left: 180° clockwise about origin
- Same as above: flip all points to opposite quadrant.

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#### 🔹 Bottom Right: 90° clockwise about origin
- Rule: (x, y) → (y, -x)

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💡 Tips for Students:

- Always label the original and rotated shapes clearly.
- Double-check signs: negative signs are easy to miss!
- Use tracing paper or a protractor if needed.
- Rotations preserve size and shape (congruent figures).

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📌 Final Answer Summary

To complete this worksheet:
1. For each shape, list the coordinates of the vertices.
2. Apply the correct rotation rule based on the instruction.
3. Plot the new points and draw the rotated image.
4. Compare with the red shape (if provided) to verify accuracy.

> ⚠️ Since the image isn’t visible, I cannot give exact answers unless you describe the shapes or provide their coordinates.

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❓ Need Help With a Specific One?

If you tell me:
- The coordinates of the blue shape in one box,
- The rotation described,

I can compute the rotated coordinates and guide you step-by-step!

Would you like to do that? Just describe one section!