Question

1. a. what transformations map the figure onto itself? 180 degrees

Explanation:

A rotation of \(180^{\circ}\) around the center of the cross - shaped figure maps it onto itself. This is because when you rotate a figure by \(180^{\circ}\), each point \((x,y)\) in the original figure is mapped to the point \((-x,-y)\). For a symmetric cross - like figure (assuming it is symmetric about its center in both the horizontal and vertical directions), after a \(180^{\circ}\) rotation, the new position of each part of the figure coincides with the original position. Also, reflections across the vertical and horizontal lines passing through the center of the figure (if the figure is symmetric about these axes) will map the figure onto itself.

Answer:

A \(180^{\circ}\) rotation about the center of the figure, and reflections across the vertical and horizontal lines passing through the center of the figure.