Question

reflecting over the y-axis:
reflecting over the y-axis rule:

write down the ordered pair for a.
if a is reflected across the y- axis, what would be the new point on the graph?
label this point.
look at both points, what observations can you make about the two points.

Explanation:

Step1: Identify point A's coordinates

From the graph, point A is at $(3, 2)$.

Step2: Apply y-axis reflection rule

For reflection over y-axis, flip x-sign: $(x,y)\to(-x,y)$.
So $(-3,2)$ is the new point.

Step3: State observations about the points

The y-values are equal; x-values are opposites.

Step4: Formalize the reflection rule

General rule: $(x,y)\mapsto(-x,y)$

Answer:

1. Ordered pair for A: $(3, 2)$
2. New reflected point: $(-3, 2)$ (label this point on the graph at $x=-3, y=2$)
3. Observations: The two points have the same y-coordinate, and their x-coordinates are additive inverses (opposites) of each other. They are symmetric with respect to the y-axis.
4. Reflecting over the y-axis rule: For any point $(x, y)$, its reflection across the y-axis is $(-x, y)$.