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I have a line between two vertices of two objects. I need to move one of them by a variable distance but always following the direction of the line.

I draw the line between the two vertices without problems, but when I try to move one of the extremities of the line this one changes the orientation.

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How can I correct my geometry nodes to make it work correctly?

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You were so close… From a difference of positions you obtained an original offset, then you normalized it for a direction, and then scaled this direction. This would work if the first point was at the origin, as it's just a direction. Otherwise "apply" this offset on the first point, to move from the first point. You do it by simply adding the offset to the first point (or the 2nd point if you want Distance=0 to mean the full line):

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