The Move Tool: axis reflection of manipulation
The move tool has the ability to reflect selection and manipulations of vertices across an axis plane.
Go to Window / Settings/Preferences / Tools Settings to change the properties of the move manipulator tool.
The dialog box looks as follows:
Scroll down inside the Tool Settings dialog until you come to Reflection Settings and hit the checkbox beside Reflection:
Select the Reflection Axis as either X, Y or Z, and experiment with it.