JOSM: How to stretch a line, and keep the direction constant?

Another solution, IMHO more straightforward than Hendrikklaas and aseerel4c26's, is to switch to extrude mode (x) and then move the node while pressing Ctrl. Shows guidelines, and lets you choose between angles when the node is connected to more than one way segment.

a bit of a workaround I use often:

• extension: select B and press key A on you keyboard twice. Then the angle snapping is active - you can easily select the 0° for placement of a new node. If you want to eliminate the original node, move it to B' and press the M key to merge both (the node id of B should be kept automatically). Screenshot just before the addition of B'.
• contraction: just insert a new node by clicking (in insert mode) on the line between A and B. Again, merge if necessary.

Warden, Use JOSM to make this happen. Copy the old line and drop it beside. Draw an extra line twice as long as you want the new one to be. Position the line by using control + shift + mouse pointer to match the direction of the old one. (try it) Draw the new one over the extra one and if it matches your desires, delete the extra one and the copy you’ve made for the original direction. Or copy and paste your old line in your usual programm, put them next to each other and join them into one line.