Geometry worksheet featuring six problems on graphing transformations of shapes, including rotations and reflections on coordinate grids.

It looks like you've uploaded a worksheet titled "Rotations of Shapes", where the task is to rotate given shapes on a coordinate grid according to specific instructions (e.g., 90°, 180°, or 270° rotations about the origin or another point). However, the image is blurry, making it difficult to read the exact details and coordinates.

But I can help guide you through how to solve rotation problems like these step by step. Let's go over the general method for rotating shapes on a coordinate plane, and then apply it to typical problems found in such worksheets.

---

🔷 General Rules for Rotations About the Origin

For any point $(x, y)$, the rules for rotation about the origin (0, 0) are:

| Rotation | Rule |
|--------|------|
| 90° counterclockwise | $ (x, y) \rightarrow (-y, x) $ |
| 90° clockwise | $ (x, y) \rightarrow (y, -x) $ |
| 180° | $ (x, y) \rightarrow (-x, -y) $ |
| 270° counterclockwise (or 90° clockwise) | $ (x, y) \rightarrow (y, -x) $ |

> Note: A 270° counterclockwise rotation is the same as a 90° clockwise rotation.

---

✔ Step-by-Step Solution Strategy

Let’s assume each problem asks you to rotate a shape (like a triangle or quadrilateral) by a certain degree around the origin or a given point.

#### Example Problem:
> Rotate triangle ABC 90° counterclockwise about the origin.

Steps:
1. Identify the coordinates of the original vertices.
- Suppose $A(2, 1), B(4, 3), C(3, 5)$
2. Apply the rotation rule:
- For 90° CCW: $(x, y) \rightarrow (-y, x)$
- So:
- $A(2,1) \rightarrow (-1, 2)$
- $B(4,3) \rightarrow (-3, 4)$
- $C(3,5) \rightarrow (-5, 3)$
3. Plot the new points and connect them to form the rotated image.

---

🔍 Common Types of Problems on This Worksheet

Based on your blurry image, here are likely types of problems:

1. Rotate 90° counterclockwise about the origin
2. Rotate 180° about the origin
3. Rotate 90° clockwise about the origin
4. Rotate 270° counterclockwise
5. Rotate about a point other than the origin (less common, but possible)

---

🧩 Example Walkthrough (Hypothetical)

Let’s say Problem 1 shows a triangle with vertices at:
- $A(-2, 1)$
- $B(-1, 3)$
- $C(1, 2)$

And the instruction is: Rotate 90° counterclockwise about the origin

Using the rule: $(x, y) \rightarrow (-y, x)$

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

Now plot these new points and draw the triangle.

---

💡 Tips for Accuracy

- Always label the original and rotated points clearly.
- Use graph paper to plot accurately.
- Check if the shape maintains size and shape (rotations are rigid transformations).
- Double-check signs — especially when rotating clockwise vs. counterclockwise.

---

❓ How to Solve Your Specific Problems?

Since the image is blurry, I can’t see the exact coordinates or directions. But here’s what you should do:

1. Identify the original shape’s vertices from the black triangle/polygon.
2. Read the rotation instruction (e.g., “rotate 90° counterclockwise”).
3. Apply the correct transformation rule.
4. Plot the new points and draw the rotated image.
5. Label the new shape clearly.

---

📝 Final Answer Format

If you were to write answers:

> Problem 1: Rotate 90° CCW about origin
> Original: $A(-2,1), B(-1,3), C(1,2)$
> Rotated: $A'(-1,-2), B'(-3,-1), C'(-2,1)$
> → Draw triangle using these new points.

---

Would you like me to simulate solving one of the problems based on the visible red/orange shapes? If so, describe the coordinates or sketch them in text (e.g., "a triangle with vertices at (-2,1), (-1,3), (1,2)") and I’ll walk you through it!