Question

Let $P(x,y)$ be any given point and $P(x_1,y_1)$ be the image of $P(x,y)$ after reflection.

The matrix of reflection of $P$ in $x$ - axis is

• A. $\left[\begin{array}{cc}1& 0\\ 0& -1\end{array}\right]$
• B. $\left[\begin{array}{cc}-1& 0\\ 0& 1\end{array}\right]$
• C. $\left[\begin{array}{cc}-1& 0\\ 0& -1\end{array}\right]$
• D. $\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

Answer 1

The correct option is A $\left[\begin{array}{cc}1& 0\\ 0& -1\end{array}\right]$

Since, $P^{\prime }\left(x_1{y}_1\right)$ is the image of p(x,y) after reflection in x -axis .

As $\therefore x_1=x=1x+0y$

& $y_1=y=0x-1y$

$\therefore \left[\begin{array}{c}{x}_1\\ y_1\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& -1\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]$

$\therefore$ Reflection of P(x, y) in x-axis is given by the matrix

$\left[\begin{array}{cc}1& 0\\ 0& -1\end{array}\right]$

$\therefore$ Choice (a) is correct.