Question

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

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

\
ight \\)
\\( \left \

$$\begin{array} { l } { 3 } \\\\ { 3 } \\end{array}$$

\
ight. \\)

Explanation:

Step1: Recall the reflection rule over the x - axis

When reflecting a point \((x,y)\) over the \(x\) - axis, the transformation 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 \(x\) - axis, it becomes \(

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

\).

Step2: Apply the rule to the given matrix

The original matrix is \(

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

\). For each column \(

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

\) in the matrix:

• For the second column \(

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

\), after reflection over the \(x\) - axis, using the rule \((x,y)\to(x, - y)\), we get \(

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

\).

Answer:

The value in the green - box (second column of the new matrix) is \(6\).