Question

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

Explanation:

Step1: Analyze coordinate changes

Compare the coordinates of points before and after reflection. For example, point L(-4, 2) is reflected to L'(-4, -2). The x - coordinate remains the same and the y - coordinate changes sign.

Step2: Recall reflection rules

The rule for reflection over the x - axis is \(r_{x - axis}(x,y)\to(x, - y)\) and for reflection over the y - axis is \(r_{y - axis}(x,y)\to(-x,y)\). Since only the y - coordinate changes sign here, it is a reflection over the x - axis.

Answer:

C. \(r_{x - axis}(x,y)\to(x, - y)\)