Question

graph the image of trapezoid tuvw after a reflection over the x - axis.

Explanation:

Step1: Recall reflection rule

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

Step2: Identify trapezoid vertices

Let's assume the coordinates of trapezoid $TUVW$ are $T(x_T,y_T)$, $U(x_U,y_U)$, $V(x_V,y_V)$, $W(x_W,y_W)$. From the graph, if $T(6,-8)$, $U(8,-8)$, $V(4,-4)$, $W(-2,-4)$.

Step3: Apply reflection rule to vertices

For point $T(6,-8)$: $(6,-8)\to(6,8)$.
For point $U(8,-8)$: $(8,-8)\to(8,8)$.
For point $V(4,-4)$: $(4,-4)\to(4,4)$.
For point $W(-2,-4)$: $(-2,-4)\to(-2,4)$.

Step4: Graph new trapezoid

Plot the new points $(6,8)$, $(8,8)$, $(4,4)$, $(-2,4)$ and connect them in order to form the reflected trapezoid.

Answer:

Graph the trapezoid with vertices $(6,8)$, $(8,8)$, $(4,4)$, $(-2,4)$ (by plotting the points and connecting them in order).