Ohio Assessments for Educators (OAE) Mathematics Practice Exam

How is a matrix reflection performed over the x-axis?

1. Through the matrix: 1 0 0 -1

2. By multiplying with the matrix: 1 0 0 -1

3. Using a dilation factor k

4. By adding to each matrix value

The correct answer is: By multiplying with the matrix: 1 0 0 -1

A matrix reflection over the x-axis involves changing the sign of the y-coordinates of the points represented by the matrix. This transformation is encapsulated by the multiplication of a point’s coordinate matrix by the reflection matrix specific for the x-axis, which is represented as: \[ \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix} \] When a point \((x, y)\) is expressed in matrix form as \(\begin{pmatrix} x \\ y \end{pmatrix}\) and then multiplied by the reflection matrix, the resulting point is: \[ \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} x \\ -y \end{pmatrix} \] This transformation shows that the x-coordinate remains the same, while the y-coordinate is inverted, achieving the reflection across the x-axis. In the context of the choices presented, multiplying by the matrix to achieve this transformation is the correct method, as it directly applies the rules