Question

On a coordinate plane, a quadrilateral has points E (negative 2, 0), D (0, 4), G (4, 2), and F (0, 0).
Which are true if figure DEFG is reflected across the x-axis? Check all that apply.

D(0, 4) → D'(0, –4)
E(–2, 0) → E'(–2, 0)
The perpendicular distance from G' to the x-axis will equal 2 units.
The perpendicular distance from D' to the x-axis will equal 8 units.
The orientation will be preserved.

Answer 1

To analyze the reflections across the x-axis for the points of quadrilateral DEFG, you follow the rule that any point \((x, y)\) when reflected across the x-axis becomes \((x, -y)\). Let's apply this to each point:

1. **Point D(0, 4)**:
- After reflecting: D' becomes (0, -4)

2. **Point E(-2, 0)**:
- After reflecting: E' becomes (-2, 0) (because the y-coordinate is 0 and remains unchanged)

3. **Point G(4, 2)**:
- After reflecting: G' becomes (4, -2)

4. **Point F(0, 0)**:
- After reflecting: F' becomes (0, 0) (also unchanged)

Now let's evaluate each statement:

1. **D(0, 4) → D'(0, –4)**:
- **True**: This is correct.

2. **E(–2, 0) → E'(–2, 0)**:
- **True**: This is correct.

3. **The perpendicular distance from G' to the x-axis will equal 2 units**:
- G' is at (4, -2). The distance from G' to the x-axis is the absolute value of the y-coordinate, which is |-2| = 2 units.
- **True**: This is correct.

4. **The perpendicular distance from D' to the x-axis will equal 8 units**:
- D' is at (0, -4). The distance from D' to the x-axis is |-4| = 4 units, not 8.
- **False**: This is incorrect.

5. **The orientation will be preserved**:
- Reflection across the x-axis does not preserve the orientation of the figure; it flips the orientation.
- **False**: This is incorrect.

In summary, the true statements are:

- D(0, 4) → D'(0, –4)
- E(–2, 0) → E'(–2, 0)
- The perpendicular distance from G' to the x-axis will equal 2 units.