The midpoint by definition is the divides a line segment in two.
This means if point Y is the midpoint of XZ, then it is equidistant from X and Z which means
[tex]XY=YZ[/tex]And since from segment addition postulate, we know that
[tex]XY+YZ=XZ[/tex]substituting XY = YZ in the above equation gives
[tex]XY+XY=XZ[/tex][tex]\rightarrow2XY=XZ[/tex][tex]\therefore XY=\frac{1}{2}XZ.[/tex]Hence, it is proved that if Y is the midpoint of XZ then XY = 1/2XZ.
