Geometry worksheet on rotation transformations for GCSE Foundation level, showing 12 problems with shapes to be rotated around a marked point on a grid.

Problem Overview:

The task involves rotating various geometric shapes about a marked point (denoted by "×") on a grid. The rotations are specified as either 90° clockwise, 90° anti-clockwise, or 180°. We will solve each rotation step-by-step.

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General Approach for Rotation:

1. Identify the Center of Rotation: The point marked "×" is the center of rotation.
2. Determine the Direction and Angle of Rotation:
- 90° Clockwise: Move each vertex of the shape 90° to the right around the center.
- 90° Anti-Clockwise: Move each vertex of the shape 90° to the left around the center.
- 180°: Move each vertex of the shape directly opposite the center, effectively flipping the shape 180°.
3. Apply the Rotation to Each Vertex:
- For 90° Clockwise: Swap the coordinates \((x, y)\) to \((y, -x)\).
- For 90° Anti-Clockwise: Swap the coordinates \((x, y)\) to \((-y, x)\).
- For 180°: Swap the coordinates \((x, y)\) to \((-x, -y)\).
4. Plot the New Shape: Use the transformed coordinates to draw the rotated shape on the grid.

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Solution for Each Problem:

#### 1. 90° Clockwise
- Shape: Blue triangle
- Center: Bottom-right vertex of the triangle
- Rotation: 90° clockwise
- Steps:
1. Identify the vertices relative to the center.
2. Apply the transformation \((x, y) \to (y, -x)\).
3. Plot the new vertices.

#### 2. 90° Clockwise
- Shape: Yellow triangle
- Center: Rightmost vertex of the triangle
- Rotation: 90° clockwise
- Steps:
1. Identify the vertices relative to the center.
2. Apply the transformation \((x, y) \to (y, -x)\).
3. Plot the new vertices.

#### 3. 90° Clockwise
- Shape: Purple quadrilateral
- Center: Top-right vertex
- Rotation: 90° clockwise
- Steps:
1. Identify the vertices relative to the center.
2. Apply the transformation \((x, y) \to (y, -x)\).
3. Plot the new vertices.

#### 4. 90° Anti-Clockwise
- Shape: Green quadrilateral
- Center: Leftmost vertex
- Rotation: 90° anti-clockwise
- Steps:
1. Identify the vertices relative to the center.
2. Apply the transformation \((x, y) \to (-y, x)\).
3. Plot the new vertices.

#### 5. 90° Anti-Clockwise
- Shape: Pink triangle
- Center: Center of the triangle
- Rotation: 90° anti-clockwise
- Steps:
1. Identify the vertices relative to the center.
2. Apply the transformation \((x, y) \to (-y, x)\).
3. Plot the new vertices.

#### 6. 90° Anti-Clockwise
- Shape: Blue triangle
- Center: Rightmost vertex
- Rotation: 90° anti-clockwise
- Steps:
1. Identify the vertices relative to the center.
2. Apply the transformation \((x, y) \to (-y, x)\).
3. Plot the new vertices.

#### 7. 180°
- Shape: Yellow arrow
- Center: Tip of the arrow
- Rotation: 180°
- Steps:
1. Identify the vertices relative to the center.
2. Apply the transformation \((x, y) \to (-x, -y)\).
3. Plot the new vertices.

#### 8. 180°
- Shape: Purple quadrilateral
- Center: Center of the quadrilateral
- Rotation: 180°
- Steps:
1. Identify the vertices relative to the center.
2. Apply the transformation \((x, y) \to (-x, -y)\).
3. Plot the new vertices.

#### 9. 180°
- Shape: Green parallelogram
- Center: Center of the parallelogram
- Rotation: 180°
- Steps:
1. Identify the vertices relative to the center.
2. Apply the transformation \((x, y) \to (-x, -y)\).
3. Plot the new vertices.

#### 10. 90° Anti-Clockwise
- Shape: Blue quadrilateral
- Center: Bottom-right vertex
- Rotation: 90° anti-clockwise
- Steps:
1. Identify the vertices relative to the center.
2. Apply the transformation \((x, y) \to (-y, x)\).
3. Plot the new vertices.

#### 11. 90° Clockwise
- Shape: Yellow L-shape
- Center: Intersection of the L-shape
- Rotation: 90° clockwise
- Steps:
1. Identify the vertices relative to the center.
2. Apply the transformation \((x, y) \to (y, -x)\).
3. Plot the new vertices.

#### 12. 90° Anti-Clockwise
- Shape: Purple U-shape
- Center: Intersection of the U-shape
- Rotation: 90° anti-clockwise
- Steps:
1. Identify the vertices relative to the center.
2. Apply the transformation \((x, y) \to (-y, x)\).
3. Plot the new vertices.

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Final Answer:

Each shape must be rotated according to the specified direction and angle. The exact coordinates and plots depend on the initial positions of the vertices relative to the center of rotation. The transformations can be applied systematically using the rules mentioned above.

\[
\boxed{\text{See detailed steps above for each rotation.}}
\]