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We need to reflect the rectangle across the line \( y = -x - 2 \) to locate the new coordinates of points \( G' \) and \( C' \). The process involves applying a geometric reflection transformation over this line.

### Steps to solve:

1. **Identify coordinates of points \( G \) and \( C \):**
   - The coordinates of \( G \) and \( C \) can be read off the graph. \( G \) seems to be at \( (-4, 2) \) and \( C \) at \( (-1, 1) \).

2. **Reflection rule for any line** \( y = -x + b \) can be generalized using the formula for reflecting across a line. However, for simplicity, the reflection across the line \( y = -x - 2 \) transforms each point \( (x_1, y_1) \) into a new point \( (x'_1, y'_1) \) that maintains equal perpendicular distance from the line.

I'll calculate the new points \( G' \) and \( C' \). Let me perform the reflection calculations.After reflecting the points across the line \( y = -x - 2 \):

- The reflection of point \( G(-4, 2) \) remains the same at \( G'(-4, 2) \).
- The reflection of point \( C(-1, 1) \) results in \( C'(-3, -1) \).

Thus, the coordinates of the reflected points are:
- \( G' = (-4, 2) \)
- \( C' = (-3, -1) \)

Would you like further clarification on these steps or additional information? Here are some related questions you might find helpful:

1. How do you find the equation of a reflection line?
2. What is the general formula for reflecting a point across a line?
3. How does reflecting across \( y = -x \) differ from other lines?
4. Can the reflection be done using matrix transformations?
5. How do you check if two points are equidistant from a line?

**Tip:** When reflecting across a line, ensure the perpendicular distance from the original point to the line is maintained for accuracy.

Reflect the rectangle in Y = -X - 2 to locate the points G' and C'.

Reflect a rectangle across the line y = -x - 2 and locate the points G' and C'. This problem involves applying reflection geometry rules. Learn how to identify points after reflection and use perpendicular distance for accuracy. Suitable for students in Grades 8-10.

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