This whole grid of nine figures looks exactly the same after it is given a half turn about its centre. Which figure belongs in the bottom-right cell?

Under a half turn of the whole grid the bottom-right cell lands on the top-left cell, and its figure is turned upside down as well. So the missing figure is the top-left figure given a half turn: the arrow moves to the lower half pointing left and the dot moves to the top-right corner: (b). Check the pairs: the bottom-middle figure is the top-middle one turned round. (a) and (c) are mirror images and (d) is not turned at all.