Coordinate geometry worksheet with four problems involving rotation of figures around the origin.

It looks like you've uploaded an image of a geometry worksheet that involves transformations of shapes on the coordinate plane. The task is to find the coordinates of the vertices of each figure after a given transformation, specifically rotations of 90° (either clockwise or counterclockwise).

However, due to the image being blurry and the text not clearly readable, I can't extract exact numbers or coordinates from it.

But I can help you solve such problems in general and guide you through how to approach them.

---

🔷 Problem Type: Rotation of Figures on Coordinate Plane

You're likely dealing with rotating a shape 90° around the origin (0,0), either:

- 90° counterclockwise
- 90° clockwise

Let’s go over the rules for rotating a point $(x, y)$ about the origin:

#### ✔ Rotation Rules:
1. 90° counterclockwise:
$$
(x, y) \rightarrow (-y, x)
$$

2. 90° clockwise:
$$
(x, y) \rightarrow (y, -x)
$$

---

🔍 Step-by-Step Approach

To solve these types of problems:

1. Identify the original coordinates of the vertices of the shape (black triangle or quadrilateral).
2. Apply the rotation rule to each vertex.
3. Plot the new points (in blue) and connect them to form the rotated image.
4. Write down the new coordinates.

---

🧩 Example

Suppose we have a triangle with vertices:

- A = (2, 1)
- B = (4, 1)
- C = (3, 3)

And we are to rotate it 90° counterclockwise about the origin.

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

- A = (2, 1) → (-1, 2)
- B = (4, 1) → (-1, 4)
- C = (3, 3) → (-3, 3)

So the new coordinates are:
- A' = (-1, 2)
- B' = (-1, 4)
- C' = (-3, 3)

---

💡 Tips for Your Worksheet

Since your worksheet shows 4 diagrams (a–d):

- Look at the original shape (in black) and rotated image (in blue).
- Identify if it's a 90° clockwise or counterclockwise rotation.
- Use the rules above to verify or compute the new coordinates.
- If the rotation is not around the origin, then you’ll need to translate, rotate, then translate back — but usually in basic problems, it's around the origin.

---

❓ What You Can Do Now

If you can describe the original coordinates or the figures in each diagram (e.g., "Figure a has a triangle with vertices at (1,1), (3,1), (2,3)"), I can help you find the transformed coordinates.

Alternatively, if you can retype the questions or describe what's written, I’ll be happy to walk you through solving them step by step.

Would you like to do that?