What is the pre-image of vertex a' if the rule that created the image is ry-axis(x, y) → (–x, y)?

 Preimage of A' is A (x,y).

Step-by-step explanation:

Suppose we have given a point A' (-x,y) and let be the rotation transformation with center of rotation at origin(0,0) such that

Now in rotation transformation of any point about y axis i.e.( ) it produces the reflected image by changing the polarity of x abscissa only and not of y. Therefore, by applying rotation transformation about y axis on image A'(-x,y) gives the pre-image of (-x,y) = (x,y) [which is the reflection of A'].

For example :- let P (1,2) be any point then after rotation transformation about y axis it will become P'(-1,2).