Question

take a look at your tables from problems 5 and 6. those points show a reflection over the y - axis. discuss: what patterns do you see between the pre - image coordinates and the image coordinates? a. complete the table for the same transformation. b. unit 1 lesson 5 33

Explanation:

Step1: Recall reflection rule over y - axis

When a point $(x,y)$ is reflected over the y - axis, the transformation rule is $(x,y)\to(-x,y)$.

Step2: Apply rule to given point

For the point $(3,1)$ reflected over the y - axis, using the rule $(x,y)\to(-x,y)$, we substitute $x = 3$ and $y=1$. So the new point is $(- 3,1)$.

Answer:

For part b, if the pre - image point is $(x,y)$, the image point after reflection over the y - axis is $(-x,y)$. For the point $(3,1)$ in the pre - image, the image point is $(-3,1)$.
For part a, the pattern between pre - image and image coordinates for a reflection over the y - axis is that the y - coordinate remains the same and the x - coordinate changes its sign. That is, if the pre - image point has coordinates $(x,y)$, the image point has coordinates $(-x,y)$.