Coordinate geometry worksheet with six graphs showing figures and transformation tasks.

Problem Analysis:

The task is to copy some shapes using transformations. The provided image shows a grid with several shapes, and the goal is to replicate these shapes in different positions or orientations using geometric transformations such as translation, reflection, or rotation.

Solution Approach:

1. Identify the Original Shapes:
- The original shapes are given in the grid.
- We need to analyze each shape and determine how it can be transformed to match the target positions.

2. Understand Transformations:
- Translation: Moving the shape to a new position without changing its orientation or size.
- Reflection: Flipping the shape over a line (axis of reflection).
- Rotation: Turning the shape around a point by a specific angle (e.g., 90°, 180°).

3. Apply Transformations:
- For each shape, decide which transformation(s) are needed to place it correctly in the target position.
- Use the grid lines to ensure accuracy in positioning.

4. Copy the Shapes:
- Replicate the shapes in their new positions based on the chosen transformations.

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Step-by-Step Solution:

#### Shape 1:
- Original Position: Top-left corner of the grid.
- Target Position: Bottom-right corner of the grid.
- Transformation: Translation.
- Move the shape down and to the right until it reaches the bottom-right corner.
- Action: Copy the shape exactly as it is, but in the new position.

#### Shape 2:
- Original Position: Center of the grid.
- Target Position: Top-right corner of the grid.
- Transformation: Reflection.
- Reflect the shape over a vertical axis passing through the center of the grid.
- Action: Flip the shape horizontally and place it in the top-right corner.

#### Shape 3:
- Original Position: Bottom-left corner of the grid.
- Target Position: Center of the grid.
- Transformation: Rotation.
- Rotate the shape 90° clockwise around its center.
- Action: Rotate the shape and place it in the center of the grid.

#### Shape 4:
- Original Position: Top-middle of the grid.
- Target Position: Bottom-middle of the grid.
- Transformation: Translation.
- Move the shape straight down to the bottom-middle of the grid.
- Action: Copy the shape exactly as it is, but in the new position.

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Final Answer:

Using the transformations described above, copy the shapes into their respective target positions on the grid. The solution involves:
1. Translating Shape 1 to the bottom-right corner.
2. Reflecting Shape 2 over a vertical axis to the top-right corner.
3. Rotating Shape 3 90° clockwise to the center.
4. Translating Shape 4 straight down to the bottom-middle.

$$
\boxed{\text{See the transformations applied as described.}}
$$

This ensures that all shapes are correctly placed according to the instructions.