https://file.aiquickdraw.com/mathbot/file/1728608790455f376bf6l.jpg

The task in the image is to reflect the given figure over the line \( y = -1 \).

### Steps to reflect a shape over the line \( y = -1 \):

1. **Identify the coordinates of the vertices** of the polygon in the image. Let's call these points \( (x_1, y_1), (x_2, y_2), (x_3, y_3), \dots \).
2. **Reflect each point across the line** \( y = -1 \). To reflect a point \( (x, y) \) over this line, the new y-coordinate is determined by the formula:
   \[
   y' = -1 - (y - (-1)) = -2 - y
   \]
   The x-coordinate remains unchanged.
3. **Plot the new points** after reflection and connect them in the same order to form the reflected shape.

#### Example of the reflection formula:
- If a point \( (x, y) \) is above the line, for example, \( y = 5 \), the reflected point would be:
   \[
   y' = -2 - 5 = -7
   \]
   So the reflected point would be \( (x, -7) \).

Would you like me to walk through the reflection of each point in the figure, or would you like further clarification?

Here are some related questions for better understanding:
1. What are the coordinates of the vertices of the original figure?
2. How do you calculate reflections over other lines, like \( y = 2 \)?
3. What is the general reflection rule for any horizontal line \( y = c \)?
4. How does the process differ for reflecting over a vertical line, like \( x = 3 \)?
5. How would this reflection change if the line of reflection was diagonal, like \( y = x \)?

**Tip:** When reflecting points over a horizontal line, only the y-coordinates change, but the x-coordinates stay the same!

Learn how to reflect a polygon over the horizontal line y = -1 with step-by-step instructions. This problem covers geometric reflections on a coordinate plane and is suitable for students in Grades 8-10.

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