Ohio Assessments for Educators (OAE) Mathematics Practice Exam

Which of the following movements does not occur during matrix reflection over the y-axis?

1. The x-coordinates of points are negated

2. The y-coordinates of points remain unchanged

3. The matrix translation occurs

4. Addition of scalar values to y-coordinates

The correct answer is: The matrix translation occurs

The correct answer highlights that matrix translation does not occur during matrix reflection over the y-axis. In a reflection across the y-axis, points that have a specific x-coordinate transform to their reflected position by negating the x-coordinate, while their y-coordinates remain unchanged. Therefore, for any point (x, y), the reflected point will be (-x, y). This transformation directly involves manipulating the x-coordinates by negating them, which answers the first part of the question. Additionally, while reflecting across the y-axis, the y-coordinates of points do not change. They stay the same, which confirms the second point. On the other hand, translation involves shifting points in a certain direction, which is not part of the reflection process. The reflection does not add or subtract values to move the point; it merely flips its position based on the y-axis. Similarly, adding scalar values to y-coordinates represents a transformation that also does not occur during simple reflection over the y-axis since the coordinates of the points do not change in this manner. Thus, identifying that matrix translation is not a component of the reflection process clarifies why it is the correct choice in this scenario.