The Create Whisker Lines from Points tool is found under the Advanced Feature Creation Options sub-menu of the Digitizer menu or context menu. To activate this option in the Advanced Feature Creation Options menu, first select a point feature or features with the Digitizer Tool.
Once activated, the Specify Length and Direction of Whisker Line dialog will appear.
Choose to specify the lines either by a fixed X and Y offset, or with a distance and bearing.
The opposite direction will be added to the whisker line as well.
See also the radial lines option in Create Range Rings / Ellipses and Create New Point/ Text Feature At Specified Bearing/ Distance for similar tools.