Question

graph the image of △tuv 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 coordinates of $\triangle TUV$

Let's assume the coordinates of $V$ are $(0,8)$, of $U$ are $(7,10)$ and of $T$ are $(7,5)$.

Step3: Apply reflection rule to $V$

For point $V(0,8)$, after reflection over the $x -$axis, the new point $V'$ has coordinates $(0,- 8)$ since using the rule $(x,y)\to(x,-y)$ with $x = 0$ and $y=8$.

Step4: Apply reflection rule to $U$

For point $U(7,10)$, after reflection over the $x -$axis, the new point $U'$ has coordinates $(7,-10)$ as $(x,y)\to(x,-y)$ with $x = 7$ and $y = 10$.

Step5: Apply reflection rule to $T$

For point $T(7,5)$, after reflection over the $x -$axis, the new point $T'$ has coordinates $(7,-5)$ as $(x,y)\to(x,-y)$ with $x = 7$ and $y=5$.

Step6: Graph the new triangle

Plot the points $V'(0,-8)$, $U'(7,-10)$ and $T'(7,-5)$ and connect them to form $\triangle T'U'V'$.

Answer:

Graph the points $(0,-8)$, $(7,-10)$ and $(7,-5)$ and connect them to get the reflected triangle.