Question

what is the rule for the reflection? m(-5,4) m(5,4) l(-6,2) n(-3,2) n(3,2) l(6,2) r_y - axis(x,y)→(-x,y) r_y - axis(x,y)→(x, - y) r_x - axis(x,y)→(-x,y) r_x - axis(x,y)→(x, - y)

Explanation:

Step1: Analyze point - coordinate changes

For point $M(-5,4)$ which becomes $M'(5,4)$, and point $N(-3,2)$ which becomes $N'(3,2)$, and point $L(-6,2)$ which becomes $L'(6,2)$. The $y$ - coordinates remain the same, and the $x$ - coordinates change their signs.

Step2: Recall reflection rules

The rule for reflection over the $y$ - axis is $r_{y - axis}(x,y)\to(-x,y)$. When reflecting a point $(x,y)$ over the $y$ - axis, the $x$ - value is negated and the $y$ - value stays the same.

Answer:

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