Question

Use the graph to answer the question.

Graph of polygon ABCD with vertices at negative 4 comma negative 5, negative 2 comma 2, 3 comma 2, 1 comma negative 5. A second polygon A prime B prime C prime D prime with vertices at negative 4 comma 5, negative 2 comma negative 2, 3 comma negative 2, 1 comma 5.

Determine the line of reflection used to create the image.

x = −2
x-axis
y = −2
y-axis

Answer 1

To determine the line of reflection used to create the image of polygon ABCD to polygon A'B'C'D', we can analyze the coordinates of the vertices of both polygons.

Original vertices of polygon ABCD:
- A(-4, -5)
- B(-2, 2)
- C(3, 2)
- D(1, -5)

Transformed vertices of polygon A'B'C'D':
- A'(-4, 5)
- B'(-2, -2)
- C'(3, -2)
- D'(1, 5)

We can check the y-coordinates of the transformation:
- The y-coordinates of points A and A' match in the x-coordinate but are reflected over which horizontal line?
- A (-4, -5) and A' (-4, 5) suggest symmetry about y = 0 (the x-axis).

- The y-coordinates of points B and B':
- B (-2, 2) and B' (-2, -2) also reflect over y = 0.

- The y-coordinates of points C and C':
- C (3, 2) and C' (3, -2) likewise confirm reflection across y = 0.

- Points D and D':
- D (1, -5) and D' (1, 5) also show symmetry about y = 0.

Each original point has a corresponding point in the image that is symmetrical with respect to the x-axis (y = 0 line). Therefore, the line of reflection used to create polygon A'B'C'D' from polygon ABCD is the **x-axis**.

The answer is:
**x-axis**