Question

graph the image of rectangle qrst 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 rectangle

Let's assume the coordinates of the vertices of rectangle $QRST$ are $Q(x_1,y_1)$, $R(x_2,y_2)$, $S(x_3,y_3)$, $T(x_4,y_4)$. From the graph, if $Q(-10,-6)$, $R(-2,-6)$, $S(-2,2)$, $T(-10,2)$.

Step3: Apply reflection rule

For point $Q(-10,-6)$, after reflection over the $y -$axis, the new point $Q'(10,-6)$.
For point $R(-2,-6)$, after reflection over the $y -$axis, the new point $R'(2,-6)$.
For point $S(-2,2)$, after reflection over the $y -$axis, the new point $S'(2,2)$.
For point $T(-10,2)$, after reflection over the $y -$axis, the new point $T'(10,2)$.

Step4: Graph the new rectangle

Plot the points $Q'(10,-6)$, $R'(2,-6)$, $S'(2,2)$, $T'(10,2)$ on the coordinate - plane and connect them to form the reflected rectangle.

Answer:

Graph the rectangle with vertices $(10,-6)$, $(2,-6)$, $(2,2)$, $(10,2)$.