Rotations of Shapes - Kuta Software - Free Printable

It looks like you've uploaded an image containing a worksheet titled "Rotations of Shapes", with several tasks asking to rotate shapes using the coordinate plane. However, I currently can't view or access images directly.

To help you, I’ll need you to describe the problems in the image — for example:

- What are the coordinates of the original shape?
- What is the center of rotation (e.g., origin, point A, etc.)?
- What is the angle and direction of rotation (e.g., 90° clockwise, 180° counterclockwise)?
- Are there specific instructions for each question?

Alternatively, if you can type out the details of one or more problems from the worksheet, I can walk you through the steps to solve them.

For now, here’s a general guide on how to rotate shapes on the coordinate plane:

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🔁 How to Rotate a Shape

#### 1. Rotation Rules (about the origin)

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

> Note: 270° clockwise = 90° counterclockwise; 270° CCW = 90° CW.

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#### 2. Steps to Rotate a Shape

1. Identify the vertices of the shape.
2. Apply the rotation rule to each vertex.
3. Plot the new points.
4. Connect the points to form the rotated image.

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#### 3. If rotating about a point other than the origin
- Translate the shape so that the center of rotation moves to the origin.
- Apply the rotation.
- Translate back.

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Example:

Suppose you have a triangle with vertices at A(1,1), B(3,1), C(2,3), and you're asked to rotate it 90° clockwise about the origin.

Apply the rule: (x, y) → (y, -x)

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

Plot these new points and connect them.

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Please provide the details of your worksheet (e.g., coordinates, rotation instructions), and I’ll solve each problem step-by-step!