Question

reflect the given triangle over the line ( y = -x ).
\begin{bmatrix} 3 & 6 & 3 \\ -3 & 3 & 3 end{bmatrix}
\begin{bmatrix} 3 & ? & \\ -3 & & end{bmatrix}

Explanation:

Step1: Recall the reflection formula

When reflecting a point \((x,y)\) over the line \(y = -x\), the transformation rule is \((x,y)\to(-y,-x)\).

Step2: Apply the formula to each point

• For the point \((6,3)\):

Using the rule \((x = 6,y = 3)\to(-y=-3,-x=-6)\).

• For the point \((3,3)\):

Using the rule \((x = 3,y = 3)\to(-y=-3,-x=-3)\).

Answer:

The completed matrix is \(

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

\)