Final answer:
Segment MN is the pre-image of M'N' after a dilation at a scale factor of 2 from the center (2, 0). MN is half the length of M'N' and is located at M (0, 0) and N (2, 0), making option (a) the correct answer.
Step-by-step explanation:
When a geometric figure is dilated, every point of the figure is moved away from or towards a fixed point (the center of dilation), by a distance proportional to its distance from the fixed point. In this case, segment M'N' is dilated from center (2, 0) by a scale factor of 2.
Starting with segment M'N', which has endpoints M' (-2, 0) and N' (2, 0), we can calculate the pre-image segment MN by considering that a dilation by a factor of 2 means each point on MN must be half as far from the center as the points on M'N'. Since the dilation center is one of the endpoints (N'), N will remain the same, i.e., N (2, 0), and only M needs to be pinpointed.
Since M' is 4 units away from the center of dilation (2, 0) in the negative x-direction, M will be half that distance in the same direction. Thus, point M lies 2 units away at M (0, 0). This means that option (a) is correct: Segment MN is located at M (0, 0) and N (2, 0) and is half the length of segment M'N'.