write the coordinates of the vertices after a reflection over the line $y = -1$.

Explanation:

Step1: Identify original coordinates

From the graph, the vertices are $P(-6, 0)$, $Q(3, 0)$, $R(3, 7)$, and $S(-6, 7)$.

Step2: Apply reflection formula

For a reflection over $y = k$, the new $y'$ is $2k - y$. $$y' = 2(-1) - y = -2 - y$$

Step3: Calculate reflected $y$-coordinates

For $P$ and $Q$: $y' = -2 - 0 = -2$. For $R$ and $S$: $y' = -2 - 7 = -9$.

Step4: State final coordinates

The $x$-coordinates remain unchanged during a reflection over a horizontal line.

Answer:

$P'(-6, -2)$ $Q'(3, -2)$ $R'(3, -9)$ $S'(-6, -9)$