Question

write the coordinates of the vertices after a reflection over the x - axis.

Explanation:

Step1: Recall reflection rule

The rule for reflecting a point $(x,y)$ over the $x -$axis is $(x,-y)$.

Step2: Identify original coordinates

Assume the original coordinates of the vertices are $E(x_1,y_1)$, $F(x_2,y_2)$, $G(x_3,y_3)$, $H(x_4,y_4)$. From the graph, if we assume $E(0, - 8)$, $F(8,-8)$, $G(8,-2)$, $H(0,-2)$.

Step3: Apply reflection rule

For point $E(0, - 8)$, after reflection over the $x -$axis, the new coordinates $E'(0,8)$ since $x = 0$ and $y=-(-8) = 8$.
For point $F(8,-8)$, after reflection over the $x -$axis, the new coordinates $F'(8,8)$ since $x = 8$ and $y=-(-8)=8$.
For point $G(8,-2)$, after reflection over the $x -$axis, the new coordinates $G'(8,2)$ since $x = 8$ and $y=-(-2)=2$.
For point $H(0,-2)$, after reflection over the $x -$axis, the new coordinates $H'(0,2)$ since $x = 0$ and $y=-(-2)=2$.

Answer:

$E'(0,8)$
$F'(8,8)$
$G'(8,2)$
$H'(0,2)$