c. The reflection of \( (-x, y) \) across the \( x \)-axis

To solve this problem, we need to understand how reflection across the x-axis affects the coordinates of a point in the Cartesian plane. When a point is reflected across the x-axis, the y-coordinate changes its sign, while the x-coordinate remains the same. In other words, if a point has coordinates (x, y), its reflection across the x-axis will have coordinates (x, -y). Now, let's apply this rule to the given point (-x, y): 1. The x-coordinate remains the same: -x. 2. The y-coordinate changes its sign: -y. Therefore, the reflection of (-x, y) across the x-axis is (-x, -y).