Question

reflect the given triangle over the line $y=-x$.
$\

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

$
$\

$$\begin{bmatrix}3&-3&\\square\\?\\end{bmatrix}$$

$
$\

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

$

Explanation:

Step1: Recall the reflection formula

The formula for reflecting a point \((x,y)\) over the line \(y =-x\) is \((x,y)\to(-y,-x)\).

Step2: Apply the formula to each point

• For the point \((3,-3)\):

Using the formula \((x = 3,y=-3)\), we get \((-(-3),-3)=(3,-3)\).

• For the point \((6,3)\):

Using the formula \((x = 6,y = 3)\), we get \((-3,-6)\).

• For the point \((3,3)\):

Using the formula \((x = 3,y = 3)\), we get \((-3,-3)\).

Answer:

\(

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

\)