If you want to move an anchor point on an object, in Illustrator, and have the lines follow without creating curves, here are the steps:
1) Create your object if you have not created one already.
2) Select the Direct Selection Tool, which the white-filled arrow from your tools palette.
3) Choose a space outside the artwork and click once. This will deselect the object.
4) Move arrow over the anchor point you want to move. A tiny square will show up indicating that you have the arrow in the right place.
5) Click and hold, and you should see the tiny square and the tail of the arrow disappear.
6) Drag anchor point where you wish to place it and release the mouse button.
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