Question

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

$$\begin{array} { c c c } { 0 } & { 7 } & { - 1 } \\\\ { 0 } & { - 3 } & { - 4 } \\end{array}$$

\
ight \\)
\\( \left \

$$\begin{array} { c c c } { 0 } & { 3 } & {? } \\\\ { 0 } & { } & { } \\end{array}$$

\
ight \\)

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 \((7,-3)\):

Using the rule \((x = 7,y=-3)\to(-y,-x)= (3,-7)\).

• For the point \((-1,-4)\):

Using the rule \((x=-1,y = -4)\to(-y,-x)=(4,1)\).

Answer:

\(

$$\begin{bmatrix}0&3&4\\0&-7&1\end{bmatrix}$$

\)