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 $P(x_1,y_1)$, $Q(x_2,y_2)$, $R(x_3,y_3)$. From the graph, if $P(-9,-2)$, $Q(-2,-2)$, $R(-6,-5)$.

Step3: Apply reflection rule to each point

For point $P(-9,-2)$, after reflection over the $y -$axis, the new point $P'(9,-2)$ since $x=- 9$ becomes $-x = 9$ and $y=-2$ remains the same.
For point $Q(-2,-2)$, after reflection, the new point $Q'(2,-2)$ as $x = - 2$ becomes $-x=2$ and $y=-2$ stays the same.
For point $R(-6,-5)$, after reflection, the new point $R'(6,-5)$ as $x=-6$ becomes $-x = 6$ and $y=-5$ remains unchanged.

Step4: Graph the new triangle

Plot the points $P'(9,-2)$, $Q'(2,-2)$ and $R'(6,-5)$ on the coordinate - plane and connect them to form the reflected triangle $\triangle P'Q'R'$.

Answer:

Graph the points $P'(9,-2)$, $Q'(2,-2)$ and $R'(6,-5)$ and connect them to get the image of $\triangle PQR$ after reflection over the $y -$axis.