To Delete a Vertex in a Polyline

Click Modify > Object > Polyline.
Select a polyline.
Enter e (Edit vertex).
The first vertex is marked with an X. Use the Next option to move the X to the vertex preceding the one that you want to delete.
Enter s (Straighten).
Use the Next option to move the X to the vertex immediately following the one that you want to delete.
Enter g (Go).
The vertex on the polyline is deleted. The vertices on either side of the deleted vertex are joined by a straight polyline segment.
Enter x (Exit) to end editing vertices.
Press Enter to end the command.