Question

the points are at: W (-2,5), A (8,5), D (-2,-2) and R (8,-1)

Examine the polygon in the figure shown. Identify a line of symmetry that will flip the figure onto itself.

(1 point)
Responses

y-axis
y -axis

y=3
𝑦
=
3
y equals 3

x-axis
x -axis

x=3

Answer 1

To identify a line of symmetry for the polygon formed by the points W (-2, 5), A (8, 5), D (-2, -2), and R (8, -1), we can analyze the positions of the points.

1. The points W and A have the same y-coordinate (5), and they are located symmetrically across the y-axis.
2. The points D and R have different y-coordinates but have the same x-coordinate (8 for R and -2 for D).

Given this arrangement, the most promising lines of symmetry are the vertical and horizontal lines.

- The **y-axis** is a potential line of symmetry because the left side (W and D) and right side (A and R) can be reflected across it.

- The line **y=3** can also be a line of symmetry since W and A are above it, and D and R are below it.

To determine if a line of symmetry is present, check if reflecting each point across the line yields another point in the set.

**Conclusion**: The correct lines of symmetry identified can be either the y-axis or the line y = 3. However, since the possibility of reflection is clear across the y-axis, it is the strongest symmetry present.

Thus, the best response is **y-axis**.

Answer 2

why is it not y=3?

Answer 3

Let's examine why the line \( y = 3 \) is not a valid line of symmetry for the polygon formed by the points W (-2, 5), A (8, 5), D (-2, -2), and R (8, -1).

### Points Breakdown:
- **W (-2, 5)** and **A (8, 5)** are both above \( y = 3 \), as they both have a y-coordinate of 5.
- **D (-2, -2)** is below \( y = 3 \) with a y-coordinate of -2.
- **R (8, -1)** is also below \( y = 3 \) with a y-coordinate of -1.

### Reflection Analysis:
1. **Reflecting W across \( y = 3 \)**:
- Distance from W (y = 5) to \( y = 3 \) is \( 5 - 3 = 2 \).
- Thus, reflecting W would give a point at \( y = 3 - 2 = 1 \), which is not represented by any point in the polygon.

2. **Reflecting A across \( y = 3 \)**:
- Similar to W, reflecting A (y = 5) would yield a point at \( y = 1 \), also not represented.

3. **Reflecting D across \( y = 3 \)**:
- Distance from D (y = -2) to \( y = 3 \) is \( 3 - (-2) = 5 \).
- Thus, reflecting D would give a point at \( y = 3 + 5 = 8 \), also not represented.

4. **Reflecting R across \( y = 3 \)**:
- Reflecting R (y = -1) would yield a point at \( y = 3 + 2 = 5 \), which corresponds to W or A, but it would not maintain symmetry with D.

### Conclusion:
When attempting to reflect the points across \( y = 3 \), their reflected locations either fall outside the set of defined points or do not maintain the shape of the original polygon. Thus, the line \( y = 3 \) does not work as a line of symmetry for this polygon.

**The most valid line of symmetry is still the y-axis**, as points on either side of the y-axis are symmetric with respect to the y-axis itself.