https://file.aiquickdraw.com/mathbot/file/1728955286291nphksde6.jpg

The task involves reflecting the triangle \( \Delta EFG \) to its image \( \Delta E'F'G' \) over the x-axis. You need to determine the coordinates of the reflected image points \( E', F', G' \), which correspond to points \( E, F, G \) after reflection.

### Coordinates of \( \Delta EFG \):
- \( E (-3, 5) \)
- \( F (-2, 2) \)
- \( G (-4, 2) \)

### Reflection rule:
When reflecting over the x-axis, the y-coordinate of each point changes sign, while the x-coordinate remains the same. The reflection formula is:
\[
(x, y) \to (x, -y)
\]

### Applying the reflection:
- For point \( E (-3, 5) \), the reflection is \( E' (-3, -5) \).
- For point \( F (-2, 2) \), the reflection is \( F' (-2, -2) \).
- For point \( G (-4, 2) \), the reflection is \( G' (-4, -2) \).

### Completed table:
| \( \Delta EFG \) | \( \Delta E'F'G' \) |
|------------------|--------------------|
| \( E (-3, 5) \)  | \( E' (-3, -5) \)  |
| \( F (-2, 2) \)  | \( F' (-2, -2) \)  |
| \( G (-4, 2) \)  | \( G' (-4, -2) \)  |

### Explanation in words:
To map \( \Delta EFG \) to \( \Delta E'F'G' \), you reflect each vertex over the x-axis. This means for every point, the x-coordinate stays the same, while the y-coordinate changes sign. For example, point \( E (-3, 5) \) is reflected to \( E' (-3, -5) \), and the same rule applies to the other points.

Would you like more details or have any questions?

### Additional questions:
1. What happens if you reflect \( \Delta EFG \) over the y-axis instead of the x-axis?
2. How would the coordinates change if you reflected the triangle over both the x- and y-axes?
3. What is the distance between point \( E \) and its reflection \( E' \)?
4. How can you use the reflection formula to determine if two points are symmetric with respect to the x-axis?
5. Can you describe the transformation if the triangle is reflected over a diagonal line like \( y = x \)?

### Tip:
Reflections maintain the size and shape of a figure, but they reverse the orientation relative to the axis of reflection.

Show how each vertex of triangle EFG maps to its image using a reflection across the x-axis. Complete the table with the coordinates of the image points E', F', and G'.

Learn how to reflect triangle EFG across the x-axis and determine the coordinates of the reflected image points. This problem involves understanding the reflection theorem and applying the formula (x, y) → (x, -y) on a coordinate plane. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation