Question

Which of the following options best describes the relationship between the segment formed by corresponding vertices and the line of reflection when performing a reflection for a pre-image over the x-axis, y-axis, line y = x, or line y = -x?

A) The segment remains unchanged.
B) The segment is rotated 90 degrees.
C) The segment is translated horizontally.
D) The segment is translated vertically.

Answer 1

When performing a reflection for a pre-image over the x-axis, y-axis, line y = x, or line y = -x, the segment formed by corresponding vertices and the line of reflection have different relationships.

Step-by-step explanation:

When performing a reflection for a pre-image over the x-axis, y-axis, line y = x, or line y = -x, the segment formed by corresponding vertices and the line of reflection have different relationships:

1. If the reflection is over the x-axis or y-axis, the segment remains unchanged. For example, if the pre-image has the points (2, 5) and (7, 5), the image will also have these points after reflection over the x-axis or y-axis.
2. If the reflection is over the line y = x or line y = -x, the segment is translated vertically. For example, if the pre-image has the points (2, 5) and (7, 5), the image after reflection over the line y = x will have the points (5, 2) and (5, 7), which have undergone a vertical translation.