Question

reflect the given triangle over the y - axis.
\\( \left \

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

\
ight \\)
\\( \left \

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

\
ight \\)

Explanation:

Step1: Recall the reflection rule over y - axis

When reflecting a point \((x,y)\) over the \(y\) - axis, the rule is \((x,y)\to(-x,y)\). In matrix form, if we have a point represented as \(

$$\begin{bmatrix}x\\y\end{bmatrix}$$

\), after reflection over the \(y\) - axis, it becomes \(

$$\begin{bmatrix}-x\\y\end{bmatrix}$$

\).

Step2: Apply the rule to the second point

The original second point in the matrix \(

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

\) is \(

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

\). Using the reflection rule \(x = 6,y = 3\), then \(-x=-6\) and \(y = 3\).

Step3: Apply the rule to the third point

The original third point in the matrix \(

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

\) is \(

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

\). Using the reflection rule \(x = 3,y = 3\), then \(-x=-3\) and \(y = 3\).

Answer:

The completed matrix is \(

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

\)