Math worksheet for practicing shape rotation on a coordinate plane.

Since I can't view or access images directly, I can’t see the specific shapes or their positions on the coordinate grids in your uploaded image. However, I can guide you through how to rotate shapes on a coordinate plane about the origin and help you solve each problem step by step based on standard rotation rules.

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🔁 Rotation Rules About the Origin

For any point $(x, y)$, rotating it around the origin follows these rules:

| Rotation | Rule |
|--------|------|
| 90° Clockwise | $(x, y) \rightarrow (y, -x)$ |
| 90° Counterclockwise | $(x, y) \rightarrow (-y, x)$ |
| 180° | $(x, y) \rightarrow (-x, -y)$ |
| 270° Clockwise (or 90° CCW) | $(x, y) \rightarrow (-y, x)$ |

> Note: 270° clockwise = 90° counterclockwise.

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Let’s go through each problem step-by-step using these rules. Since I don’t have the actual coordinates of the shapes, I’ll explain how to do it. You can apply this method to each shape.

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✔ Step-by-Step Guide

#### 1) 180° Rotation
- For every vertex $(x, y)$ of the shape:
- New coordinates: $(-x, -y)$
- Plot the new points and connect them.

#### 2) 90° Clockwise Rotation
- For each point $(x, y)$:
- New coordinates: $(y, -x)$
- Example: If a point is at $(3, 2)$ → becomes $(2, -3)$

#### 3) 90° Counterclockwise Rotation
- For each point $(x, y)$:
- New coordinates: $(-y, x)$
- Example: $(3, 2)$ → $(-2, 3)$

#### 4) 180° Rotation
- Same as #1: $(-x, -y)$

#### 5) 90° Clockwise
- Use rule: $(x, y) \rightarrow (y, -x)$

#### 6) 90° Counterclockwise
- Use rule: $(x, y) \rightarrow (-y, x)$

#### 7) 180° Rotation
- Again: $(-x, -y)$

#### 8) 90° Clockwise
- Use: $(x, y) \rightarrow (y, -x)$

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🧩 How to Apply This to Your Image

1. Identify the vertices of each shape.
2. Write down their coordinates from the grid.
3. Apply the correct rotation rule based on the problem.
4. Plot the new points on the same grid.
5. Connect the new points to form the rotated image.

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🔍 Example (Illustrative)

Suppose in Problem 1, the shape has vertices at:
- $A(2, 3)$
- $B(3, 1)$
- $C(1, 1)$

And we are doing a 180° rotation:

- $A(2, 3) \rightarrow A'(-2, -3)$
- $B(3, 1) \rightarrow B'(-3, -1)$
- $C(1, 1) \rightarrow C'(-1, -1)$

Now plot $A'$, $B'$, $C'$ and draw the triangle.

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✔ Tips for Accuracy

- Always rotate each vertex, not just the whole shape.
- Double-check signs when applying rules.
- Use graph paper carefully — keep track of quadrants.

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📝 Final Advice

Since I can’t see the image, please describe one of the shapes and its coordinates, or list the vertices of a shape, and I can show you exactly how to rotate it.

Alternatively, if you can describe what each shape looks like (e.g., "a triangle with vertices at (1,2), (3,2), (2,4)") and the rotation requested, I’ll walk you through the full solution.

Let me know which problem you’d like help with!