Question

what is the rule for the reflection?
$r_{y - axis}(x,y)\to(-x,y)$
$r_{y - axis}(x,y)\to(x, - y)$
$r_{x - axis}(x,y)\to(-x,y)$
$r_{x - axis}(x,y)\to(x, - y)$

Explanation:

Step1: Analyze the transformation

Observe the original hexagon and its reflected image. Points above the x - axis are moved to below the x - axis and vice - versa. The x - coordinates of the points remain the same and the y - coordinates change their signs.

Step2: Recall reflection rules

The rule for reflection over the x - axis is \(r_{x - axis}(x,y)=(x, - y)\).

Answer:

D. \(r_{x - axis}(x,y)=(x, - y)\)