https://file.aiquickdraw.com/mathbot/file/17280678920612qyhr9ii.jpg

To reflect the image across the line \( x = -2 \), we need to use the following reflection rule for coordinates:

If a point \((x, y)\) is reflected over the line \( x = -2 \), the new x-coordinate becomes:

\[
x' = -2 - (x - (-2)) = -2 - (x + 2) = -x - 4
\]

Thus, the new x-coordinate of the reflected point will be:

\[
x' = -4 - x
\]

The y-coordinate will remain the same. Now let's calculate the reflection for each point \( D, E, F \):

### Step 1: Coordinates of \( D, E, F \)
From the image, the coordinates of \( D, E, F \) appear to be:

- \( D(3, 3) \)
- \( E(6, 1) \)
- \( F(2, -1) \)

### Step 2: Reflect each point over \( x = -2 \)
Using the formula \( x' = -4 - x \), reflect each point:

- For \( D(3, 3) \):
  \[
  x' = -4 - 3 = -7 \quad \text{so} \quad D'( -7, 3)
  \]
  
- For \( E(6, 1) \):
  \[
  x' = -4 - 6 = -10 \quad \text{so} \quad E'( -10, 1)
  \]
  
- For \( F(2, -1) \):
  \[
  x' = -4 - 2 = -6 \quad \text{so} \quad F'( -6, -1)
  \]

### Step 3: Select the correct option
None of the provided answers exactly match the correct reflection coordinates. However, based on the reflection process, you can manually input the correct answers if needed.

Would you like more details or have further questions?

Here are 5 questions to further explore:
1. How do you reflect a shape across any arbitrary vertical line?
2. What changes when reflecting over a horizontal line instead?
3. How do transformations like translation and rotation differ from reflection?
4. Can you identify the rule for reflecting across the line \( x = 0 \)?
5. How does reflecting over diagonal lines differ from vertical or horizontal?

**Tip:** When reflecting over vertical lines like \( x = -2 \), only the x-coordinate changes, while the y-coordinate stays the same.

Reflect this image across the line x = -2. What are the coordinates of D', E', and F'?

Learn how to reflect a triangle across the vertical line x = -2. This problem involves coordinate geometry and the reflection transformation, using the formula x' = -4 - x to calculate new coordinates for points D, E, and F.

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