Question

what is the pre - image of vertex a created the image is r_y - axis(x, y) a(-4, 2) a(-2, -4) a(2, 4) a(4, -2)

Explanation:

Step1: Recall reflection rule

The rule for reflecting a point $(x,y)$ over the $y -$axis is $(x,y)\to(-x,y)$. To find the pre - image, we reverse the process.

Step2: Analyze the image point

Let the image point $A'$ have coordinates $(2,4)$. Using the reverse of the $y -$axis reflection rule, if the image is $(x,y)=(2,4)$, then the pre - image $(x_0,y_0)$ satisfies $x_0=-x$ and $y_0 = y$. So the pre - image is $(- 2,4)$. But if we assume there is a mis - typing in the problem setup and we consider the general rule application, if the image point has $x = 2$ and $y=4$, the pre - image under $y$-axis reflection is $(-2,4)$. Among the given options, if we assume the image point $A'$ has coordinates such that when we apply the reverse of $y$-axis reflection rule, for an image point $(x,y)$ the pre - image is $(-x,y)$. If we assume the image of $A$ after $y$-axis reflection is $(2,4)$, the pre - image is $(-2,4)$. If we assume the image point is considered in a different way and we know that for $y$-axis reflection $(x,y)\to(-x,y)$, if the image has positive $x = 2$ and positive $y = 4$, the pre - image has $x=-2$ and $y = 4$.

Answer:

There seems to be an error in the options as the correct pre - image of a point $(2,4)$ (assuming $A'$ has coordinates $(2,4)$) under $y$-axis reflection should be $(-2,4)$ which is not in the given options. If we assume the closest correct logic application and there is a mis - print in options, we note the concept of $y$-axis reflection rule $(x,y)\to(-x,y)$ for finding pre - image. If we assume the image point $A'$ has $x = 2$ and $y = 4$, the pre - image should have $x=-2$ and $y = 4$.