Geometric transformations
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Find the image of the point \((2,3)\) under each of the following transformations
i) A reflection in the \(x\)-axis
ii) A reflection in the \(y\)-axis
$$\begin{aligned}\text{(i)}\quad &\left[\begin{array}{l}x^{\prime} \\ y^{\prime}\end{array}\right]=\left[\begin{array}{cc}1 & 0 \\ 0 & -1\end{array}\right]\left[\begin{array}{l}2 \\ 3\end{array}\right]=\left[\begin{array}{c}2 \\ -3\end{array}\right] \rightarrow(2,-3)\\
\text{(ii)}\quad &\left[\begin{array}{l}x^{\prime} \\ y^{\prime}\end{array}\right]=\left[\begin{array}{cc}-1 & 0 \\ 0 & 1\end{array}\right]\left[\begin{array}{l}2 \\ 3\end{array}\right]=\left[\begin{array}{c}-2 \\ 3\end{array}\right] \rightarrow(-2,3)
\end{aligned}$$
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