Question

graph the image of kite tuvw 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 vertices of kite TUVW

Let's assume the coordinates of the vertices of kite TUVW are $T(x_T,y_T)$, $U(x_U,y_U)$, $V(x_V,y_V)$, $W(x_W,y_W)$.

Step3: Find new coordinates after reflection

The new coordinates after reflection over the $x -$axis will be $T'(x_T,-y_T)$, $U'(x_U,-y_U)$, $V'(x_V,-y_V)$, $W'(x_W,-y_W)$.

Step4: Plot new points

Plot the points $T'$, $U'$, $V'$, $W'$ on the coordinate - plane and connect them in the order to form the reflected kite.

Since we don't have the actual coordinates of the vertices of the kite TUVW given in the problem (only the graph is shown without labeled coordinates), we can't give the exact numerical coordinates of the reflected kite. But the general process is as above. If we had the coordinates, for example, if $T(- 2,-9)$, $U(0,-6)$, $V(-2,-3)$, $W(-8,-6)$:
For point $T(-2,-9)$, after reflection over the $x -$axis, $T'(-2,9)$.
For point $U(0,-6)$, after reflection over the $x -$axis, $U'(0,6)$.
For point $V(-2,-3)$, after reflection over the $x -$axis, $V'(-2,3)$.
For point $W(-8,-6)$, after reflection over the $x -$axis, $W'(-8,6)$. Then we would plot these new points to get the reflected kite.

Answer:

Plot the points obtained by applying the $(x,y)\to(x, - y)$ rule to each vertex of the kite TUVW on the coordinate - plane and connect them to form the reflected kite.