Question

graph the image of △pqr 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 coordinates of $\triangle PQR$

Let's assume $P(x_1,y_1)$, $Q(x_2,y_2)$ and $R(x_3,y_3)$. From the graph, if $P(-8, - 2)$, $Q(-2,-2)$ and $R(-6,-4)$.

Step3: Apply reflection rule to each point

For point $P(-8,-2)$, after reflection over the $y -$axis, the new point $P'(8,-2)$ since $x=-8$ becomes $-x = 8$ and $y=-2$ remains the same.
For point $Q(-2,-2)$, after reflection over the $y -$axis, the new point $Q'(2,-2)$ as $x = - 2$ becomes $-x=2$ and $y=-2$ stays the same.
For point $R(-6,-4)$, after reflection over the $y -$axis, the new point $R'(6,-4)$ because $x=-6$ becomes $-x = 6$ and $y=-4$ is unchanged.

Step4: Graph the new triangle

Plot the points $P'(8,-2)$, $Q'(2,-2)$ and $R'(6,-4)$ on the coordinate - plane and connect them to form $\triangle P'Q'R'$.

Answer:

Graph the triangle with vertices $P'(8,-2)$, $Q'(2,-2)$ and $R'(6,-4)$ on the given coordinate - plane.