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 vertices of square TUVW

Let's assume the coordinates of the vertices of square 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 $T(-8,- 10)$, $U(-4,-10)$, $V(-4,-4)$, $W(-8,-4)$.

Step3: Apply reflection rule to each vertex

For $T(-8,-10)$, after reflection over the $y -$axis, the new point $T'(8,-10)$ since $x=-8$ becomes $-(-8) = 8$ and $y=-10$ remains the same.
For $U(-4,-10)$, the new point $U'(4,-10)$.
For $V(-4,-4)$, the new point $V'(4,-4)$.
For $W(-8,-4)$, the new point $W'(8,-4)$.

Step4: Graph the new square

Plot the points $T'(8,-10)$, $U'(4,-10)$, $V'(4,-4)$, $W'(8,-4)$ and connect them to form the new square.

Answer:

Graph the square with vertices $(8,-10)$, $(4,-10)$, $(4,-4)$, $(8,-4)$