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There are two ways to do this - the results do differ by the way the attachment point behaves when you move the ends of the target line.

Method 1:

A. Create your first line.
B. Create a second line and drag the end to attach it to the first line. A magnet will be created at the point you connect the line. You can drag the magnet anywhere to position it.
C. When you move the end points of the first line, the entire line will move and drag the attached lines with it (important difference relative to method below)

Method 2:

A. Depending on your Preference setting for Line Label Creation in General preferences, you will either double or you will option-double click a line to add an extra point (=magnet) anywhere on the line's length.
B. Attach any secondary lines to this magnet.
C. Drag the ends of the first line and this time, only the end of the line will be moved. Your additional point(s) and the attached lines will stay where they were.