Asegment is dilated by a factor of 2.5 and the resulting segment is parallel to the original segment.
which statement must be true?
the center of dilation is not on the original segment.
the center of dilation is on the original segment.
the center of dilation is the midpoint of the resulting segment.
the center of dilation is the midpoint of the original segment.

  The center of dilation is not on the original segment.

Step-by-step explanation:

The center of dilation is the only invariant point. If the original segment and the dilated segment have no points in common (are parallel), then the center of dilation cannot be on either the original segment or the dilated segment.

graph b

step-by-step explanation:

one solution- graph a (clear intercepting point.)

no solution- graph b (they're parallel, there will never be a point of interception.)

infinite solutions- graph c (all points intercept.)