Find the matrix that represents a certain transformation - High school Algebra I Exercises

What is the transformation matrix that represents a counterclockwise rotation of 90^\circ through the origin?

\begin{pmatrix} 0 & 1 \cr\cr 1 & -1 \end{pmatrix}

\begin{pmatrix} 0 & -1 \cr\cr 1 & -1 \end{pmatrix}

\begin{pmatrix} 0 & -1 \cr\cr 1 & 0 \end{pmatrix}

\begin{pmatrix} 0 & 1 \cr\cr 1 & 1 \end{pmatrix}

What is the transformation matrix that represents a clockwise rotation of 45^\circ through the origin?

\begin{pmatrix} -\dfrac{\sqrt{2}}{2}& \dfrac{\sqrt{2}}{2} \cr\cr \dfrac{\sqrt{2}}{2} & -\dfrac{\sqrt{2}}{2} \end{pmatrix}

\begin{pmatrix} -\dfrac{\sqrt{2}}{2}& \dfrac{\sqrt{2}}{2} \cr\cr -\dfrac{\sqrt{2}}{2} & \dfrac{\sqrt{2}}{2} \end{pmatrix}

\begin{pmatrix} \dfrac{\sqrt{2}}{2}& \dfrac{\sqrt{2}}{2} \cr\cr -\dfrac{\sqrt{2}}{2} & \dfrac{\sqrt{2}}{2} \end{pmatrix}

\begin{pmatrix} -\dfrac{\sqrt{2}}{2}& \dfrac{\sqrt{2}}{2} \cr\cr \dfrac{\sqrt{2}}{2} & \dfrac{\sqrt{2}}{2} \end{pmatrix}

What is the transformation matrix that represents a clockwise rotation of 360^\circ through the origin?

\begin{pmatrix} -1&0 \cr\cr 0 & -1 \end{pmatrix}

\begin{pmatrix} 1&0 \cr\cr 0 & -1 \end{pmatrix}

\begin{pmatrix} 1&0 \cr\cr 0 & 1 \end{pmatrix}

\begin{pmatrix} -1&0 \cr\cr 0 & 1 \end{pmatrix}

What is the transformation matrix that represents a reflection through the origin?

\begin{pmatrix} 0 & 1 \cr\cr 1 & -1 \end{pmatrix}

\begin{pmatrix} 0 & -1 \cr\cr 1 & 0 \end{pmatrix}

\begin{pmatrix} -1& 0 \cr\cr 0 & -1 \end{pmatrix}

\begin{pmatrix} 0 & 1 \cr\cr 1 & 0 \end{pmatrix}

What is the transformation matrix that represents a reflection through the x -axis?

\begin{pmatrix} 1 & 0 \cr\cr 0 & -1 \end{pmatrix}

\begin{pmatrix} 0 & -1 \cr\cr 1 & -1 \end{pmatrix}

\begin{pmatrix} 0 & -1 \cr\cr 1 & 0 \end{pmatrix}

\begin{pmatrix} 0 & 1 \cr\cr 0 & 1 \end{pmatrix}

What is the transformation matrix that represents a reflection through the y -axis?

\begin{pmatrix} -1 & 0 \cr\cr 0 & 1 \end{pmatrix}

\begin{pmatrix} 1 & 0 \cr\cr 0 & -1 \end{pmatrix}

\begin{pmatrix} 0 & -1 \cr\cr 1 & 0 \end{pmatrix}

\begin{pmatrix} -1 & 0 \cr\cr 0 & -1 \end{pmatrix}

What is the transformation matrix that represents a reflection through the line y=x

\begin{pmatrix} -1 & 0 \cr\cr 0 & 1 \end{pmatrix}

\begin{pmatrix} 1 & 0 \cr\cr 0 & -1 \end{pmatrix}

\begin{pmatrix} 0 & -1 \cr\cr 1 & 0 \end{pmatrix}

\begin{pmatrix}0 & 1 \cr\cr 1 & 0 \end{pmatrix}