Why do I need a single line? Simple: I want my text to be centered on this line or arc.
I was trying to do a simple sign and thought I would use a centerline, draw lines out different distances to the side and then mirror them. Since I wanted to put text to a line and have it centered on the sign, nothing was allowing me to “join” or “merge” these two segments as one line. There exists instructions on the internet showing it to be a command. Either that/those command(s) have been eliminated or it is only in the purchased subscription. I decided it had to be simple. The answer was sort of simple but a bit strange to get to the end result. It involves the “extend” command. Thru this I also learned more about the “extend” command.
Here goes. Making a single line, mirroring it and then making it one line:
I now “extend” the line with a simple click. After this extension this is, indeed, a single line:
If you encounter the intermediate line segments, you just have to keep clicking until you have extended to the end.
Here is what happens with the simple little line added and you attempt to “extend”, 2 clicks and it jumps to the end of the line so no biggie. But this help to understand what “extend” is doing:
Now the arc is a bit more complicated if you want a perfectly symmetric arc: And you would if you were centering it on a sign. The only arc that will extend or mirror perfectly is a tangent arc. Therefore, you need to make a line that the arc will target as the tangent line (construction or solid line).
Now at this point, we could do this in one step by merely extending the line. Since it is perfectly tangent at the apex, it will be a symmetrical line whether we mirror or extend.
This is what would happen with “extend” if the horizontal constraining line is removed. It uses the next possible intersecting line to stop it:
So, in the end, I did not use any arc in my sign. I just wanted to figure out how to make two lines a single line and it was only logical to want to know how to make two arcs a single arc. Right? 
Here is the simple sign I was making:
Edit: My family felt the eyes made them uneasy (that is what I was going for!!!), so I had to come up with another version:
As you see, in the end, I really didn’t use my lines as intended but I now know what is going on with the “extend” command. So it was a good lesson for me.
