Educational worksheet on reflections of shapes on a coordinate grid, showing transformations across axes and a mirror line.

Problem Analysis:

The task involves understanding reflections of shapes across different lines (axes and custom mirror lines) on a coordinate grid. We need to identify the reflections of given shapes and then perform specific reflections as instructed.

#### Step 1: Identify the Reflections
We are given four shapes (a kite, a trapezium, a parallelogram, and an octagon) and their reflections. The goal is to match each shape with its reflection based on the provided options:
- x-axis
- y-axis
- mirror line crossing (2,0)

#### Step 2: Analyze Each Shape and Its Reflection
1. Kite (Green Shape):
- Original: Located in the top-left quadrant.
- Reflection: Located in the bottom-right quadrant.
- Observation: The reflection is symmetric about the y-axis. Each point on the kite is mirrored horizontally across the y-axis.

2. Trapezium (Blue Shape):
- Original: Located in the bottom-left quadrant.
- Reflection: Located in the top-right quadrant.
- Observation: The reflection is symmetric about the x-axis. Each point on the trapezium is mirrored vertically across the x-axis.

3. Parallelogram (Blue Shape):
- Original: Located in the bottom-left quadrant.
- Reflection: Located in the top-right quadrant.
- Observation: The reflection is symmetric about the mirror line crossing (2,0). This line is vertical and passes through the point (2,0). Each point on the parallelogram is mirrored across this vertical line.

4. Octagon (Blue Shape):
- Original: Located in the top-right quadrant.
- Reflection: Located in the bottom-right quadrant.
- Observation: The reflection is symmetric about the x-axis. Each point on the octagon is mirrored vertically across the x-axis.

#### Step 3: Match Shapes with Their Reflections
Based on the observations:
- Kite is reflected across the y-axis.
- Trapezium is reflected across the x-axis.
- Parallelogram is reflected across the mirror line crossing (2,0).
- Octagon is reflected across the x-axis.

#### Step 4: Perform Additional Reflections
We are asked to draw where the parallelogram and the octagon will be if:
1. The parallelogram is reflected in the mirror line that passes through point (2,0).
- This is already shown in the image. The parallelogram's reflection is correctly depicted in the top-right quadrant.

2. The octagon is reflected in the x-axis.
- The original octagon is in the top-right quadrant.
- To reflect it across the x-axis, we take each point of the octagon and change its y-coordinate to its negative value while keeping the x-coordinate the same.
- For example, if a point on the octagon is at (8, 9), its reflection will be at (8, -9).

#### Final Answer:
- Kite: Reflected across the y-axis.
- Trapezium: Reflected across the x-axis.
- Parallelogram: Reflected across the mirror line crossing (2,0).
- Octagon: Reflected across the x-axis.

For the additional reflections:
- The parallelogram's reflection is already shown in the image.
- The octagon's reflection can be drawn by mirroring it vertically across the x-axis.

\boxed{\text{Kite: y-axis, Trapezium: x-axis, Parallelogram: mirror line crossing (2,0), Octagon: x-axis}}