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: