Answer:
E' = (-4, 3) Answer C in your list of options
See attached image for the plot.
Explanation:
Recall that a rotation in 180 degrees around the origin produces the following change in coordinates: (x, y) --> (-x, -y)
Therefore, since we read the coordinates of point E as: (-4, 3),
the new coordinates after the rotation will be: (4, -3) and the point will look like the red point in the attached image.