Reflect the point worksheet for geometry practice.

Since the user has set all options (ExplainAnswer, TeachTopic, GeneratePractice) to false, I will proceed directly to providing the final answer based on the visible content of the worksheet.

The worksheet asks to graph the reflection of points across various lines. Since no specific points are given in the image (the grids are blank), I cannot solve for specific coordinates. However, I can provide the general rule for each type of reflection shown on the worksheet, which is what the student would need to apply if points were provided.

Here are the rules for reflecting a point $(x, y)$:

1. Reflection across the line $y = 1$:
* The x-coordinate stays the same.
* The y-coordinate changes so that the distance to the line $y=1$ is preserved on the other side.
* Formula: $(x, y) \rightarrow (x, 2 - y)$

2. Reflection across the y-axis:
* The y-coordinate stays the same.
* The x-coordinate changes sign.
* Formula: $(x, y) \rightarrow (-x, y)$

3. Reflection across the line $x = -1$:
* The y-coordinate stays the same.
* The x-coordinate changes so that the distance to the line $x=-1$ is preserved on the other side.
* Formula: $(x, y) \rightarrow (-2 - x, y)$

4. Reflection across the line $y = -1$:
* The x-coordinate stays the same.
* The y-coordinate changes so that the distance to the line $y=-1$ is preserved on the other side.
* Formula: $(x, y) \rightarrow (x, -2 - y)$

5. Reflection across the line $y = 4$:
* The x-coordinate stays the same.
* The y-coordinate changes so that the distance to the line $y=4$ is preserved on the other side.
* Formula: $(x, y) \rightarrow (x, 8 - y)$

6. Reflection across the line $x = 4$:
* The y-coordinate stays the same.
* The x-coordinate changes so that the distance to the line $x=4$ is preserved on the other side.
* Formula: $(x, y) \rightarrow (8 - x, y)$

7. Reflection across the line $x = -2$:
* The y-coordinate stays the same.
* The x-coordinate changes so that the distance to the line $x=-2$ is preserved on the other side.
* Formula: $(x, y) \rightarrow (-4 - x, y)$

8. Reflection across the line $y = -2$:
* The x-coordinate stays the same.
* The y-coordinate changes so that the distance to the line $y=-2$ is preserved on the other side.
* Formula: $(x, y) \rightarrow (x, -4 - y)$

Final Answer:
To solve this worksheet, you need to reflect given points across specific lines. Since no points are plotted on the grids in the image, here are the rules you would use if you had a point $(x, y)$:

1. Reflection across $y = 1$: New point is $(x, 2-y)$
2. Reflection across y-axis: New point is $(-x, y)$
3. Reflection across $x = -1$: New point is $(-2-x, y)$
4. Reflection across $y = -1$: New point is $(x, -2-y)$
5. Reflection across $y = 4$: New point is $(x, 8-y)$
6. Reflection across $x = 4$: New point is $(8-x, y)$
7. Reflection across $x = -2$: New point is $(-4-x, y)$
8. Reflection across $y = -2$: New point is $(x, -4-y)$

For horizontal lines ($y = k$), the x-value stays the same, and the new y-value is $2k - y$.
For vertical lines ($x = k$), the y-value stays the same, and the new x-value is $2k - x$.
For the y-axis ($x = 0$), just flip the sign of the x-value.