Question

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

Explanation:

Step1: Recall reflection rule

When reflecting a point $(x,y)$ over the $x - axis$, the rule is $(x,y)\to(x, - y)$.

Step2: Identify original coordinates

Let's assume the original coordinates of the vertices are $U(x_1,y_1)$, $T(x_2,y_2)$, $S(x_3,y_3)$, $R(x_4,y_4)$. From the graph, if $U=(0, - 3)$, $T=(6,-3)$, $S=(6,-9)$, $R=(3,-9)$.

Step3: Apply reflection rule

For point $U$: $(0,-3)\to(0,3)$
For point $T$: $(6,-3)\to(6,3)$
For point $S$: $(6,-9)\to(6,9)$
For point $R$: $(3,-9)\to(3,9)$

Answer:

The new coordinates of $U$ is $(0,3)$, of $T$ is $(6,3)$, of $S$ is $(6,9)$, of $R$ is $(3,9)$