Question

graph the image of rectangle klmn 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 points

Let's assume the coordinates of the vertices of rectangle $KLMN$ are $K(2,3)$, $L(5,3)$, $M(5,8)$, $N(2,8)$.

Step3: Apply reflection rule to $K$

For point $K(2,3)$, after reflection over the $y -$axis, the new point $K'$ has coordinates $(- 2,3)$.

Step4: Apply reflection rule to $L$

For point $L(5,3)$, after reflection over the $y -$axis, the new point $L'$ has coordinates $(-5,3)$.

Step5: Apply reflection rule to $M$

For point $M(5,8)$, after reflection over the $y -$axis, the new point $M'$ has coordinates $(-5,8)$.

Step6: Apply reflection rule to $N$

For point $N(2,8)$, after reflection over the $y -$axis, the new point $N'$ has coordinates $(-2,8)$.

Step7: Graph new rectangle

Plot the points $K'(-2,3)$, $L'(-5,3)$, $M'(-5,8)$, $N'(-2,8)$ and connect them to form the reflected rectangle.

Answer:

Graph the rectangle with vertices $(-2,3)$, $(-5,3)$, $(-5,8)$, $(-2,8)$ on the coordinate - plane.