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 between polygon ABCD and its image A'B'C'D', we can analyze the coordinates of both sets of vertices.

The original polygon ABCD has vertices:
- A(-4, -5)
- B(-2, 2)
- C(3, 2)
- D(1, -5)

The image polygon A'B'C'D' has vertices:
- A'(-4, 5)
- B'(-2, -2)
- C'(3, -2)
- D'(1, 5)

Now, we can compare the y-coordinates of corresponding points:
- For point A and A', the transformation is from (-5) to (5), which reflects across the line y = 0 (the x-axis) because it moves up 10 units.
- For point B and B', the transformation is from (2) to (-2), which also reflects over the x-axis because it moves down 4 units.
- For point C and C', the transformation is from (2) to (-2), which reflects over the x-axis similarly, moving down 4 units.
- For point D and D', the transformation is from (-5) to (5), reflecting upward across the x-axis with a distance of 10 units.

Since all corresponding points reflect symmetrically across the x-axis, the line of reflection used to create the image A'B'C'D' from ABCD is the **x-axis**.

So, the correct answer is **x-axis**.