Question

quadrilateral WXYZ is reflected across the line y=x to create quadrilateral W’X’Y’Z'. What are the coordinates of quadrilateral W’X’Y’Z'.

Answer 1

Explanation

We are required to determine the coordinates of W’X’Y’Z' when WXYZ is reflected across the line y = x.

This is achieved thus:

From the image, we can deduce the following:

$\begin{gathered} W(-7,3) \\ X(-5,6) \\ Y(-3,7) \\ Z(-2,3) \end{gathered}$

We know that the following reflection rules exist:

Therefore, we have:

$\begin{gathered} (x,y)\to(y,x) \\ W(-7,3)\to W^{\prime}(3,-7) \\ X(-5,6)\to X^{\prime}(6,-5) \\ Y(-3,7)\to Y^{\prime}(7,-3) \\ Z(-2,3)\to Z^{\prime}(3,-2) \end{gathered}$

Hence, the answers are:

$\begin{gathered} \begin{equation*} W^{\prime}(3,-7) \end{equation*} \\ \begin{equation*} X^{\prime}(6,-5) \end{equation*} \\ \begin{equation*} Y^{\prime}(7,-3) \end{equation*} \\ \begin{equation*} Z^{\prime}(3,-2) \end{equation*} \end{gathered}$

This is shown in the graph bwlow for further undertanding: