What is the image of a point after reflection over the y-axis?

The image of a point after reflection over the y-axis has its x-coordinate negated, while the y-coordinate remains unchanged.

When you reflect a point over the y-axis, you essentially flip it to the opposite side of the y-axis. Imagine you have a point with coordinates (x, y). After reflecting this point over the y-axis, the new coordinates will be (-x, y). This means that if the original point was to the right of the y-axis, the reflected point will be to the left, and vice versa. The y-coordinate stays the same because the reflection does not affect the vertical position of the point.

For example, if you have a point at (3, 4), reflecting it over the y-axis will move it to (-3, 4). Similarly, a point at (-5, -2) will be reflected to (5, -2). This transformation is useful in various mathematical problems and graphical representations, as it helps to understand symmetry and coordinate changes.

In summary, reflecting a point over the y-axis is a straightforward process: you simply change the sign of the x-coordinate while keeping the y-coordinate the same. This concept is fundamental in coordinate geometry and helps in visualising how shapes and points behave under different transformations.