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I am attempting to move an object a set distance in a direction relative to the objects current position. In other words I want the object to move to whatever point is 144 pixels below the object, and then stop moving. How can I do this?

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144 pixels is a very relative thing. Firstl the closer the viewer is to an object the more pixels the obj takes, therefore the less its gonna move. Secondly the resolutions changes from one pc to another (or phone to another). Third, if the object is not on the screen, it isn't gonna move.

I suggest you just take the object's current position and decrease it how much you want. Every engine will let you do it, on Unity you can use transform.position. Google it so you can be sure of what you're doing

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