Final answer:
The pre-image of segment c prime d prime, which was dilated to twice its size from the center (3, 0), is segment cd located at c(-1, 0) and d(3, 0), which is half the length of segment c prime d prime.
Step-by-step explanation:
The student's question involves determining the pre-image of a segment after a dilation with a given scale factor. Given that segment c prime d prime has endpoints c²(-5, 0) and d²(3, 0), and it was dilated from center (3, 0) by a scale factor of 2, the pre-image, which is segment cd, would have been located closer to the center before the dilation.
If we apply the scale factor in reverse, considering that the dilation made the segment larger, we find that the original segment cd would be half the length of the dilated segment c prime d prime. Therefore, if c prime is at -5 and the center is 3, the pre-image point c would have had to be midway between -5 and 3, which is at -1 (since -5 is 8 units away from 3 and half of 8 is 4, subtracting 4 from 3 gives us -1). The point d remains unchanged because it is the center of dilation. Thus, option (1), Segment cd is located at c(-1, 0) and d(3, 0) and is half the length of segment c prime d prime, is the correct description of the pre-image.