Question. A wire horizontally over a bench has one end fixed and the other end holding some weight. The weight stretches the wire to produce some extension, say $\Delta x$. Someone puts a length marker somewhere on the wire except the two ends, and this marker indicates some extension, say $\delta x$. Does $\Delta x=\delta x$? If so, why does every point of the wire get extended by the same amount?
My attempt. If thinking about fixing one end of the wire and measuring how much the other end extends upon tension, I totally accept this notion of extension. However, how could every point on the wire get extended by the same amount? I am confused. Intuitively, I feel like every point of the wire contributes some extension which add up to the total extension. Any kind of help would be appreciated!