Which transformation involves changing the sign of the x coordinate?

The transformation that changes the sign of the x-coordinate is reflection over the y-axis. When a point (x, y) is reflected over the y-axis, its new coordinates become (-x, y). This means that the x-coordinate is effectively negated, while the y-coordinate remains unchanged.

In contrast, dilation involves resizing an object without changing its shape, which does not inherently affect the signs of the coordinates. A rotation of 90 degrees would change the coordinates in a more complex way, specifically moving them to their new positions based on the original angles. Translation simply shifts a point or shape in a particular direction but does not alter the signs of the coordinates themselves. Therefore, reflection over the y-axis is the specific transformation that directly changes the sign of the x-coordinate.