ANSWERS: 3

say the perpendicular distance between the two lines is x.. . . it is a translation of one line of distance x on the perpendicular ray between the two lines.. sorry if this is vague or incorrect im not a mathematitian. . lol

If these are infinite parallel lines, then any motion which takes any two points X and Y on the first line onto the second line will do. There are rather a lot of those, even if you allow only for rigid motion. The simplest is to move X along the straight line XA to the closest corresponding point A on the second line, while keeping Y in relative position with X. XA will be perpendicular to both lines. This is a translation (but other translations would do). A more complex example would be to move the mid point of XY to an arbitrary point on the second line and then rotate X and Y 180 degrees about any axis through the mid point which is perpendicular to the second line. And a still more complex example is to pick up the first line, throw it out of the window, go downstairs, pick it up, take it back up stairs and then place it over the second line.

Reflection perfectly between the two lines.
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