Question

Use to reflect over the x-axis. Identify the transformed vector.

Answer 1

To reflect the given matrix over the x-axis, you have to multiply both matrices:

`\begin{bmatrix}{1} & {0} \\ {0} & {-1}\end{bmatrix}\cdot\begin{bmatrix}{7} \\ {-12}\end{bmatrix}`

Multiply each term of the first row of the first matrix with the corresponding terms of the column of the second matrix and add the results:

Repeat the process for the second row of the first matrix

The resulting matrix is:

`\begin{bmatrix}{1} & {0} \\ {0} & {-1}\end{bmatrix}\cdot\begin{bmatrix}{7} \\ {-12}\end{bmatrix}=\begin{bmatrix}{(1\cdot7)+(0\cdot-12)} \\ {\square}(0\cdot7)+(-1\cdot-12)\end{bmatrix}=\begin{bmatrix}{7} \\ {12}\end{bmatrix}`

The correct option is option D.