The correct answer is:
180° rotation.
Explanation:
Comparing the points D, E and F to D', E' and F', we see that the x- and y-coordinates of each have been negated, but they are still in the same position in the ordered pair.
A 90° rotation counterclockwise will take coordinates (x, y) and map them to (-y, x), negating the y-coordinate and swapping the x- and y-coordinates.
A 90° rotation clockwise will map coordinates (x, y) to (y, -x), negating the x-coordinate and swapping the x- and y-coordinates.
Performing either of these would leave our image with a coordinate that needs negated, as well as needing to swap the coordinates back around.
This means we would have to perform the same rotation again; if we began with 90° clockwise, we would rotate 90 degrees clockwise again; if we began with 90° counter-clockwise, we would rotate 90 degrees counterclockwise again. Either way this rotates the figure a total of 180° and gives us the desired coordinates.
