Question

the rule for any glide reflection over the y-axis is:
(x, y) → x + a, -(y + b).
(x, y) → -(x + a), y + b.
none of the choices are correct.

Explanation:

Step1: Recall glide reflection rule

A glide reflection over the \(y -\)axis is a combination of a reflection over the \(y -\)axis and a translation. The reflection over the \(y -\)axis has the rule \((x,y)\to(-x,y)\). Let the translation be \((x,y)\to(x + h,y + k)\). For a glide - reflection over the \(y -\)axis, first reflect: if we have a point \((x,y)\), after reflection over the \(y -\)axis it is \((-x,y)\), then translate. If the translation is \(h=-a\) (horizontal translation) and \(k = b\) (vertical translation), the rule is \((x,y)\to(-x - a,y + b)=[-(x + a),y + b]\)

Answer:

\((x,y)\to[-(x + a),y + b]\)