Question

reflect the given triangle over the line y = x.
\\( \left \

$$\begin{array} { r r r } { 3 } & { 6 } & { 3 } \\ { - 3 } & { 3 } & { 3 } \\end{array}$$

\
ight \\)
\\( \left \

$$\begin{array} { c } { - 3 } \\ { 3 } \\end{array}$$

\
ight. \\)

Explanation:

Step1: Recall reflection formula

When reflecting a point \((x,y)\) over the line \(y = x\), the new point is \((y,x)\).

Step2: Apply formula to each column

For the first column \(

$$\begin{bmatrix}3\\-3\end{bmatrix}$$

\), after reflection over \(y = x\) it becomes \(

$$\begin{bmatrix}-3\\3\end{bmatrix}$$

\).
For the second column \(

$$\begin{bmatrix}6\\3\end{bmatrix}$$

\), after reflection over \(y = x\) it becomes \(

$$\begin{bmatrix}3\\6\end{bmatrix}$$

\).
For the third column \(

$$\begin{bmatrix}3\\3\end{bmatrix}$$

\), after reflection over \(y = x\) it becomes \(

$$\begin{bmatrix}3\\3\end{bmatrix}$$

\).

Answer:

\(

$$\begin{bmatrix}-3&3&3\\3&6&3\end{bmatrix}$$

\)