91Ó°ÊÓ

An ordered pair $\left(x,y\right)$is represented by a column matrix $\left[\begin{array}{c}x\\ y\\ \end{array}\right]$which is known as vertex matrix of an ordered pair.

Since, a rectangle has 4 ordered pair on vertices so required matrix has 2 rows and 4 columns.

First row represent $x-\text{coordinate}$ and second row represents $y-\text{coordinate}$ of each vertex.

As coordinates of the vertices of rectangle are $A\left(-4,4\right),B\left(4,4\right),C\left(4,-4\right),\text{and}D\left(-4,-4\right)$

Write each ordered pair as a column of a matrix to get

Vertex matrix of new rectangle after reflection over the x -axis is product matrix $\left[\begin{array}{cc}1& 0\\ 0& -1\\ & \end{array}\right]$with vertex matrix of given rectangle as shown below

$\left[\begin{array}{cc}1& 0\\ 0& −1\end{array}\right]×\left[\begin{array}{cccc}−4& 4& 4& −4\\ 4& 4& −4& −4\end{array}\right]=\left[\begin{array}{cccc}−4& 4& 4& −4\\ −4& −4& 4& 4\end{array}\right]$

Vertex matrix of new rectangle after reflection over the y -axis is product matrix $\left[\begin{array}{cc}-1& 0\\ 0& 1\\ & \end{array}\right]$with vertex matrix of rectangle as shown below

$\left[\begin{array}{cc}−1& 0\\ 0& 1\end{array}\right]×\left[\begin{array}{cccc}−4& 4& 4& −4\\ −4& −4& 4& 4\end{array}\right]=\left[\begin{array}{cccc}4& −4& −4& 4\\ −4& −4& 4& 4\end{array}\right]$