Question

reflect the given triangle over the line ( y = -x ).
\begin{bmatrix} 0 & 7 & -1 \\ 0 & -3 & -4 end{bmatrix}
\begin{bmatrix} 0 & ? & \\ 0 & & 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 the point \((7,-3)\)

For the point with \(x = 7\) and \(y=-3\), substitute into the formula \((-y,-x)\).
We get \(-y=-(-3) = 3\) and \(-x=-7\).

Answer:

The value in the green - box (corresponding to the \(x\) - coordinate after reflection of the point \((7,-3)\)) is \(3\).