Two parallel lines are also parallel to the x-axis. consider the properties of transformations of parallel lines. do you think it is possible to use a single transformation to map the lines to themselves?

Yes it is possible. If the lines are parallel that means that using one translation would map the lines onto each other. You could also use a reflection to map the lines onto each other. The line of reflection would have to be in between your parallel lines and at the same distance from both of them. You could also use a rotation of 180 degrees to map one line onto the other.