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

Let the original coordinate of a point in the figure be \((x, y)\). 1. Reflecting \((x, y)\) across the \(x\)-axis changes the sign of the \(y\)-coordinate: \[ (x, y) \rightarrow (x, -y) \] 2. Next, reflecting \((x, -y)\) across the line \(x=0\) (the \(y\)-axis) changes the sign of the \(x\)-coordinate: \[ (x, -y) \rightarrow (-x, -y) \] The overall transformation sends \((x, y)\) to \((-x, -y)\). This is equivalent to a rotation of the original figure by \(180\) degrees about the origin. Thus, the new image is best described as: \( \textbf{(A) rotated about the origin} \).