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 original points

Let's assume the coordinates of the vertices of kite $TUVW$ are $T(x_T,y_T)$, $U(x_U,y_U)$, $V(x_V,y_V)$, $W(x_W,y_W)$. For example, if $T$ has coordinates $(- 1,-9)$, $U$ has coordinates $(1,-6)$, $V$ has coordinates $(-1,-3)$ and $W$ has coordinates $(-8,-6)$.

Step3: Apply reflection rule

The new coordinates of $T'$ will be $(x_T,-y_T)$, for our example $T'(-1,9)$. The new coordinates of $U'$ will be $(x_U,-y_U)$, so $U'(1,6)$. The new coordinates of $V'$ will be $(x_V,-y_V)$, so $V'(-1,3)$. The new coordinates of $W'$ will be $(x_W,-y_W)$, so $W'(-8,6)$.

Step4: Plot new points

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

Answer:

Graph the new kite with vertices obtained by reflecting the original vertices over the $x -$axis using the rule $(x,y)\to(x, - y)$.