Reflection and Rotation Matrices

Reflect ($4$, $3$) in the $x$-axis using $\left(\begin{array}{cc}1& 0\\ 0& -1\end{array}\right)$.

• 1Multiply: top entry = ($1\times 4$) + ($0\times 3$) = $4$. Bottom entry = ($0\times 4$) + ($-1\times 3$) = $-3$

Answer: ($4$, $-3$)

Rotate ($2$, $5$) by $90$° anticlockwise about the origin using $\left(\begin{array}{cc}0& -1\\ 1& 0\end{array}\right)$.

• 1Multiply: top entry = ($0\times 2$) + ($-1\times 5$) = $-5$. Bottom entry = ($1\times 2$) + ($0\times 5$) = $2$

Answer: ($-5$, $2$)