Symmetrize

shortcut ALT + X in edit curve mode

The Symmetrize tool is used to mirror the active spline across the curve object's local X, Y or Z axis.
Optionally the Cursor origin an orientation can be used to mirror across it and along its axes.

flick symmerizing to the left, in the negative X direction, with redundant point removal, highlighted in red

Selection

• an active spline

Statusbar

The statusbar at the bottom of Blender - after invoking the tool - provides all the info you need in regards to what keys you can press to modify the tool's behavior.

Using Symmetrize

• Invoke Symmetrize from the Menu, or using the Keymap
• Move the mouse to align with the direction, you want to mirror the active spline in
• Move it further beyond the flick ring, to execute the symmetrize operation and create the new mirrored spline
• Using C you can toggle cursor-space symmetrizing
• When redundant points are created on the mirror-plane, you have the option to toggle removal of these using R
• With the modal active, and so the flick ring visible, you can adjust your view normally, which can be helpful to pick the correct axis, or better preview the result