Snap to mid-point

[Acorn]

A Xara straight line has no mid-point as it can be transformed into a curved one at any time.

Clone and Rotate 90⁰. The crossing is the mid-point, to which you can Snap.
Clone and Scale 50%. Align end point. Mid-point is then the other end of the halved line.

The mid-point of a curved line is far more intriguing.
You could add a Point and Break there and keep approximating as. as each Line or segment has a Perimeter (P).
I would make a Text Column of pattern 1234567890 and then Fit Text to Curve. Count the numbers along the line and halve to get to the mid-point.
Accurate to about 5px but could be improved.

Acorn