Question

what is the rule for the reflection? f_x - axis(x,y)=(-x,y) f_y - axis(x,y)=(-x,y) f_x - axis(x,y)=(x, - y) f_y - axis(x,y)=(x, - y)

Explanation:

Step1: Recall reflection rules

Reflection over the x - axis changes the sign of the y - coordinate. That is, the rule for reflection over the x - axis is $r_{x - axis}(x,y)=(x, - y)$. Reflection over the y - axis changes the sign of the x - coordinate, with the rule $r_{y - axis}(x,y)=(-x,y)$.

Step2: Analyze the given points

For example, if a point $(x,y)$ is reflected over the x - axis, its image is $(x, - y)$. Looking at the general form of the rules given in the options, we can see that the rule for reflection over the x - axis is $r_{x - axis}(x,y)=(x, - y)$.

Answer:

$r_{x - axis}(x,y)=(x, - y)$ (the third option in the multiple - choice list)