Question

graph the image of square tuvw after a reflection over the y - axis.

Explanation:

Step1: Recall reflection rule

The rule for reflecting a point $(x,y)$ over the $y - axis$ is $(-x,y)$.

Step2: Identify original points

Assume $T(-7,4)$, $U(-3,4)$, $V(-3,8)$, $W(-7,8)$.

Step3: Apply reflection rule to $T$

For point $T(-7,4)$, after reflection over the $y - axis$, the new point $T'(7,4)$ since $x=-7$ becomes $-(-7) = 7$ and $y = 4$ remains the same.

Step4: Apply reflection rule to $U$

For point $U(-3,4)$, after reflection, the new point $U'(3,4)$ as $x=-3$ becomes $-(-3)=3$ and $y = 4$ is unchanged.

Step5: Apply reflection rule to $V$

For point $V(-3,8)$, after reflection, the new point $V'(3,8)$ as $x=-3$ becomes $3$ and $y = 8$ stays the same.

Step6: Apply reflection rule to $W$

For point $W(-7,8)$, after reflection, the new point $W'(7,8)$ as $x=-7$ becomes $7$ and $y = 8$ is unchanged.

Step7: Graph new square

Plot points $T'(7,4)$, $U'(3,4)$, $V'(3,8)$, $W'(7,8)$ and connect them to form the reflected square.

Answer:

Graph the square with vertices $T'(7,4)$, $U'(3,4)$, $V'(3,8)$, $W'(7,8)$