The guy here walked seven miles north, then he realized he went seven miles in the wrong direction, so he went nine miles in the opposite direction, and then he realized he went one mile too far, so he went and turned to the same direction he started in, and went one mile. Gladly, he finally found where he needed to go.
Think of this as a word problem: A boy walks seven miles north from his house. He realizes he was supposed to go one mile south of his house, and turns around. This time, he traveled nine miles south. How many miles and in what direction does he need to go in order to get to the desired destination?
Let's see. Walk seven miles north, and you are seven miles north of the original destination. (We know it sounds a little wacky, but just to make a point.) Now, you waltz nine miles south. Nine minus seven equals two. You are now two miles south of your original destination. So, in order to get to the desired location, you have to go one more mile north.
Now that you are there, you need to know how to get home. Take the solution above (Walk seven miles north, nine miles south, one mile north.) Now you are one mile south of your home. So, in order to get home, you need to go one mile north, because you are south of home.