2. 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

When a figure is reflected across the \( x \)-axis, all the \( y \)-coordinates of its points change signs. For example, a point \((x, y)\) becomes \((x, -y)\). Then, reflecting across the line \( x=0 \) (which is the \( y \)-axis) will change the signs of the \( x \)-coordinates, transforming the point into \((-x, -y)\). So, the final image ends up being a reflection of the original figure in both the \( x \)-axis and the \( y \)-axis. This final transformation is equivalent to rotating the original figure 180 degrees about the origin. So, the answer is (A) rotated about the origin!