If a figure is reflected across the \( x \)-axis, and then the image is reflected across the line \( x=0 \), what will the new image look like? (A) rotated about the origin (B) the same as the original (C) reflected across the \( y \)-axis (D) reflected across the \( x \)-axis

First, reflecting a figure across the \( x \)-axis will flip it vertically, changing the sign of the \( y \)-coordinates. For instance, a point \((x, y)\) becomes \((x, -y)\). Next, reflecting this new image across the line \( x=0 \) will flip it horizontally, changing the sign of the \( x \)-coordinates, leading to the point \((-x, -y)\). Thus, the final image will be reflected across the \( y \)-axis and flipped vertically. This series of transformations can be visualized more easily using a simple diagram or even a graphing tool. By tracing the reflections step-by-step, you can see how the points shift on the grid—making it clear that yes, the original figure appears as a mirror image of itself, but also flipped over the \( y \)-axis. So, the answer here is (C) reflected across the \( y \)-axis.