Question

finding a pre - image vertex. what is the pre - image of vertex a if the rule that created the image is r_y - axis(x, y)→(-x, y)? a(-4, 2) a(-2, -4) a(2, 4) a(4, -2)

Explanation:

Step1: Identify the rule for y - axis reflection

The rule for reflection over the y - axis is $(x,y)\to(-x,y)$. To find the pre - image from the image, we reverse the operation. If the image point is $A'(x',y')$ and the pre - image is $A(x,y)$, then $x=-x'$ and $y = y'$.

Step2: Determine the coordinates of $A'$

From the graph, the coordinates of $A'$ are $(- 2,4)$. Let $x'=-2$ and $y' = 4$.

Step3: Calculate the pre - image coordinates

Using $x=-x'$ and $y = y'$, when $x'=-2$, then $x=-(-2)=2$, and $y = 4$. So the pre - image of $A'$ is $A(2,4)$.

Answer:

A(2,4)