If A has coordinates (2, -4) and is reflected over the y-axis, find the coordinates ofA'.

1. ### Break Down the Problem

To find the coordinates of point $A'$ after reflecting point $A$ over the y-axis, we need to understand how reflection works in this context.

2. ### Relevant Concepts

When a point $(x, y)$ is reflected over the y-axis, the x-coordinate changes its sign while the y-coordinate remains unchanged. Thus, the formula for reflection over the y-axis is: $A' = (-x, y)$

3. ### Analysis and Detail

Given point $A$ has coordinates: $A(2, -4)$ Applying the reflection formula, we find:

• The x-coordinate of $A$ is $2$, so the reflected x-coordinate is $-2$.
• The y-coordinate of $A$ is $-4$, which remains unchanged.

Thus, the new coordinates after reflection $A'$ are: $A' = (-2, -4)$

4. ### Verify and Summarize

The reflection process has been verified correctly. The x-coordinate changed sign, and the y-coordinate remained the same. The final coordinates for point $A'$ are confirmed.

Final Answer

The coordinates of $A'$ are $(-2, -4)$.