Question

write the coordinates of the vertices 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 coordinates

From the graph, the coordinates of point $K$ are $(-9,-5)$, of point $L$ are $(-9,5)$, of point $M$ are $(-6,5)$ and of point $N$ are $(-6,-5)$.

Step3: Apply reflection rule to $K$

For $K(-9,-5)$, after reflection over the $y - axis$, the new $x$-coordinate is $-(-9) = 9$ and the $y$-coordinate remains $-5$. So the new coordinates of $K$ are $(9,-5)$.

Step4: Apply reflection rule to $L$

For $L(-9,5)$, after reflection over the $y - axis$, the new $x$-coordinate is $-(-9)=9$ and the $y$-coordinate remains $5$. So the new coordinates of $L$ are $(9,5)$.

Step5: Apply reflection rule to $M$

For $M(-6,5)$, after reflection over the $y - axis$, the new $x$-coordinate is $-(-6) = 6$ and the $y$-coordinate remains $5$. So the new coordinates of $M$ are $(6,5)$.

Step6: Apply reflection rule to $N$

For $N(-6,-5)$, after reflection over the $y - axis$, the new $x$-coordinate is $-(-6)=6$ and the $y$-coordinate remains $-5$. So the new coordinates of $N$ are $(6,-5)$.

Answer:

$K(9,-5)$
$L(9,5)$
$M(6,5)$
$N(6,-5)$