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A line segment is unique because unlike a regular line that goes on forever in both directions, a line segment has a starting point and an end point.
Yes. In fact, if they are not the same plane, then they must intersect in a unique straight line.
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It the point is on the line the distance is 0. If the point is not on the line, then it is possible to draw a unique line from the point to the line which is perpendicular to the line. The distance from the point to the line is the distance along this perpendicular to the line.
Two distinct (different) points are needed to determine a line.